v a c t o k fc 

* OR tOMPUTifotj 

PRIMARY IRAVPRS) POSITIONS 


'i Alt RPCLAMATlON 

Auf.} in, tj xAs 



X. 


























































V 

































THE STATE OF TEXAS 
RECLAMATION DEPARTMENT 
AUSTIN 


A227-218-1000 


Bulletin No. 8 June, 1918 


FACTORS 

FOR .THE INTERCONVERSION OF 

. LATITUDES AND DEPARTURES IN FEET 


AND 




. > 4 ) 


AUSTIN 

STATE RECLAMATION DEPARTMENT 
1918 

Mo*n o f'Td ph 













-f\ s~' 

,Y\i 


















\ 




i ' 
< • 





i> ’ > j 
? -» 
> j? > 

























EXPLANATION. 


The factors designated by the letters M and P, without reciprocals 
and in logarithmic form only, were originally designed by Mr. D. H. 
Baldwin of the United States Geological Survey, and published as 
“Logarithms and Factors for Converting Latitudes and Departures in 
Feet to Seconds of Latitude and Longitude, etc.” 

The M and P factors given herein were suggested by Mr. Baldwin’s 
tables, and were especially prepared for the use of the State Reclamation 
Department for computing geodetic traverse positions by means of the 
multiplying machine. Consequently the factors and their reciprocals 
are given in the form of natural numbers. The logarithms of the fac¬ 
tors are given chiefly in the interest of completeness. 

The M and P factors are based upon the complete formulas developed 
by the United States Coast and Geodetic Survey for computing the 
latitude and longitude of points located by primary triangulation. (See 
Coast and Geodetic Survey Special Publication No. 8, Washington, 
1911.) But as primary traverses usually consist of numerous short 
distances (or “courses”), and as it is not generally necessary to compute 
the geodetic co-ordinates of each individual traverse course, the fol¬ 
lowing described modifications are made to facilitate the traverse com¬ 
putations : 

(1) The computing is done by sections consisting of a number of 
short courses. ( 2 ) In the computation for latitude only the first term 
of the triangulation formula is used. (3) In the computation for 
longitude the complete formula is used, but the mid-latitude of the 
computing section is taken as an argument for the factor P. 

These modifications introduce small theoretical errors in the traverse 
computing, but they are altogether negligible from a practical stand¬ 
point even in a long series of computing sections, (1) when each com¬ 
puting section consists of one short course, or a number of short courses 
all having the same general direction; and ( 2 ) when each computing 
section is less than two miles long. 

When a traverse course is more than two miles long it should be com¬ 
puted as triangulation, using the complete formulas for that purpose. 
In this very rare case the M and P factors are, of course, not suitable 
for making the computation. 

The theory of the M and P factors is briefly discussed by Mr. Bald¬ 
win in the introduction to his tables. 



The purpose of the factor M is to convert differences of latitude 
(sometimes called “northings” and “southings”), in feet, into seconds 
of latitude. This is accomplished by multiplying the appropriate tab¬ 
ular value for the factor M hv the number of feet in the northing or 
southing. 

The purpose of the factor P is to convert differences of longitude 
(sometimes called “eastings” and “westings”), in feet, into seconds of 
longitude. This is accomplished by multiplying the appropriate tab¬ 
ular value for the factor P by the number of feet in the easting or 
westing. 

The purpose of the reciprocals of the factors M and P is to facilitate 
the reverse of the two foregoing operations; namely, that of converting 
differences of latitude and longitude in seconds into differences of lati¬ 
tude and departure in feet. This is accomplished by multiplying the 
appropriate tabular value for the reciprocals of the factors M and P 
by the differences in latitude and longitude in seconds. 

In the tables of the factors M and P and Keciprocal M and P the 
latitude at which the factors apply is printed in even degrees at the 
tops of the pages; in even minutes in the first left-hand column of the 
pages. The factors M and P in natural numbers are given in the 
second and third columns of the left-hand pages; the reciprocals of 
them in the second and third columns of the right-hand pages; and 
the logarithms of the factors in the fourth and fifth columns of the 
right-hand pages.. The tables for interpolating the factor P are printed 
in smaller type to the right on the left-hand pages; those for interpo¬ 
lating the factor Reciprocal P in the middle of the right-hand pages. 

In the interpolating tables'for the factor P and for the factor Recip¬ 
rocal P, the figures in the right-hand columns headed respectively 

“diff. P” and “diff. rep. P” are the numerical changes in the factors 

corresponding to the number of seconds given in the several other 
columns to the left, headed “Tabular Differences.” The figures at the 
tops of these several columns denote the total tabular changes in the 
factors for one minute. To obviate the necessity of dividing by. two in 
obtaining the factor for the average of two latitudes, the seconds in 

the table are based upon 120 instead of 60. For example (page 54), 

when 50 is the total tabular difference in the factor P for one minute, 
for a change of 1 in P the change in seconds is 120" divided by 50, 
or 2.4"; for 2 it is 4.8"; for 3 it is 7.2", i etc. Or, for a. change of 
.4 in P the change in seconds is 1.2"; for 14 it is 3.6"; for 24 it is 
6.0", etc. But as it is more convenient to mark factor numbers by 


unit changes, the tables are arranged (“staggered”) so that for any 
number of seconds less than 1.2 the change in P is 0; for 1.2" or more, 
but less than 3.6", it is 1; for 3.6" or more, but less than 6.0", it is 2, 
etc. The figures in the seconds column mark the dividing line between 
unit changes in the factors. The same plan is followed in the tables 
for interpolating the factor Reciprocal P. 

In the computation to determine latitude it is customary to select 
the factor M from the table by using as an argument the even minute 
latitude nearest to the latitude of the known point, as the tabular values 
for this factor change slowly. 

In the computation to determine longitude the factor P is selected 
from the table by using as an argument the mid-latitude of the com¬ 
puting section, or the average of the latitudes of the old point previously 
established and the new point being computed. 

In the computation to determine latitude in feet (northing or south¬ 
ing) from the difference of latitude in seconds between two points, the 
factor Reciprocal M may be selected from the table by using as an 
argument the even minute latitude nearest to the latitude midway be¬ 
tween the two points. 

In the computation to determine departure in feet (easting or west¬ 
ing) from the difference of latitude in seconds between the two points, 
the factor Reciprocal P is selected from the table by using as an argu¬ 
ment the average of the two latitudes of the two points. 

The use of the interpolating tables for the factor P is illustrated by 
the following examples: The factor P depends upon the average of 
two latitudes, and two cases arise: first, when the number of minutes 
is the same in both latitudes; and, second, when the minutes differ. 
For example, in the first case (omitting the decimals and adopting the 
nearest second) the two latRudes are: 32° 14' 57" and 32° 14' 01". 
From the main table (page take the tabular value of P correspond¬ 
ing to 32° 14',— .0116416, to which must be added a certain amount, 
obtained from the interpolating tables thus: Add the two numbers of 
seconds (57" + 01" = 58"). This sum (58") is the double average 
of the seconds in the two latitudes, and is the argument for P in the 
interpolating table, as the table is bagej. upon the double average of 
the seconds. In the main table (page 46) the total tabular difference 
between 32° 14' and 32° 15' being 21, the interpolating table (same 
page) in the column headed 21 and corresponding to 58" gives 10 as 
the change in P. Adding this correction (10) to the partial value first 
taken out of the tables (.0116416) gives the. factor value for the true 


5 


average of the two latitudes, or, P = .0116426. In the second case, 
namely, when the minutes in the two latitudes differ, two conditions 
arise in obtaining the double average of the seconds: (a) when the 
sum of the two numbers of seconds is greater than 60; and (b) when 
it is less than 60. Example in (a) : The two latitudes are: 41° 49' 57" 
and 41° 50' 51". Add the seconds, 57" + 51" = 108". subtract 60" 
from the sum, 108" — 60" — 48", which is the double average of the 
seconds and the argument for P in the interpolating table. Adopting 
the larger number of minutes (50), the argument for P in the main 
table is 41° 50', which (page^W} corresponds to .0132093. The total 
tabular difference between 41° 50' and 41° 51' being 34, the interpo¬ 
lating table (same page), in the column headed 34, and corresponding 
to 48", gives 14 as the change in P. Hence the factor P for the true 
average of the two latitudes = .0132093 + .0000014 == .0132107. 

Example in (b) : The two latitudes are 41° 49' 22" and 41° 50' 09". 
Add the seconds, 22" + 09" = 31". Adding 60" to the sum (31" + 
60" = 91") the double average of the seconds = 91", which is the argu¬ 
ment for P in the interpolating table. Adopting the lesser number of 
minutes (49), the argument for P in the main table is 41° 49', corre¬ 
sponding to .0132059. In the interpolating table 91" corresponds to 26. 
Then .0132059 + .0000026 = .0132085, = P for the true average of 
the two latitudes. 

The foregbing examples will also serve to illustrate the use of the 
interpolating tables for the factor Reciprocal P, except that, as will be 
seen by inspection of the tables, the correction corresponding to the 
double average of the seconds is always subtracted in the case of the 
Reciprocal P. 

All the tabular values are expressed in decimal places sufficient to 
insure a degree of accuracy in computing consistent with the most 
accurate class of field work. 

The use of the M and P factors and their reciprocals in natural num¬ 
bers will be illustrated by the following examples: 

I. Knowing the latitude and longitude of one point, and the dis¬ 
tances in feet north or south and east or west to. a new point, to obtain 
the M and P factors from the tables and determine the latitude and 
longitude of the new point. 

riven ■! Known point A, lat. 32° 44' 16.448"; long. 96° 56' 20.282". 

T v n I New point B, 2321.74 feet south of A; 236:28 feet east of A. 

Required, the latitude and longitude of new point B. 


6 


Computation. 


Distance (latitude) = 2321.74 feet 
south. 

Distance (departure) = 236.28 feet 
east. 

Factor M for lat. of known point 
(32° 44') - .0098947. 

Factor P for mid-la t. (32° 44' 05") 

= .0117064. 

Distance X factor M = difference in 
latitude = 22.973". 

Distance X factor P = difference in 
longitude = 2.766". 

Lat. 32° 44' 16.448" Position of 96° 56' 20.282" Long. 

Known Point A 

( + if north; — if south) Differences in seconds ( -f if west- — if east) 

—22.973. —2.766. 

Lat. 32° 43' 53.475" Resulting Position of 96° 56' 17.516" Long. 

New Point B 


II. Knowing the latitudes and longitudes of two points, to obtain the 
factors Reciprocal M and Reciprocal P, and determine the distances in 
feet north or south and east or west between the two points. 

Civen i Point A > lat 32 ° 40 ' 16 - 510 "i long. 96 ° 20 ' 39.415". 

T ( Point B, lat. 32° 40' 36.472"; long. 96° 20' 52.418". 

Required^ the distance in feet from A to B, north and south, and 
from A to B, east and west. 


Computation. 


Lat. 32° 40' 16.510" 

Point A 

96° 20' 39.415" Long. 

19.962 

Differences in i 

seconds 13.003 

Lat. 32° 40' 36.472" 

Point B 

96° 20' 52.418" Long. 

Reciprocal M for lat. 32° 40' 
= 101.063 


Rep. P for mid.-lat. 32° 40' 26", 

= 85.482 

Reciprocal M = 101.063 X 
19.962 = 2017.4 feet 


Reciprocal P = 85.482 X 
13.003 = 1111.5 feet 

2017.4 feet north and south 
tween A and B 


1111.5 feet east and west be¬ 
tween A and B 


These tables were designed and computed by Messrs. James P. Murray 
and John B. Upchurch, technical assistants of the State Reclamation 
Department. 



Austin, June, 1918. 


Arthur Alvord Stiles, 
State Reclamation Engineer. 






















25 ° 


/ 

M 

P 

/ 

0 

.0099061 

.0108694 

0 

1 

1 

708 

1 

2 

1 

723 

2 

3 

1 

738 

3 

4 

0 

752 

4 

5 

0 

767 

5 

6 

0 

782 

6 

7 

.0099060 

797 

7 

8 

.0099059 

811 

8 

9 

9 

826 

9 

10 

.0099059 

.0108841 

10 

11 

9 

856 

11 

12 

9 

871 

12 

13 

8 

885 

13 

14 

8 

900 

14 

15 

8 

915 

15 

16 

8 

930 

16 

17 

7 

945 

17 

18 

7 

960 

18 

19 

7 

975 

19 

20 

.0099057 

.0108989 

20 

21 

•7 

.0109004 

21 

22 

6 

019 

22 

23 

6 

034 

23 

24 

6 

049 

24 

25 

6 

064 

25 

26 

5 

079 

26 

27 

5 

094 

27 

28 

5 

109 

28 

29 

5 

124 

29 

30 

.0099055 

.0109139 

30 

31 

4 

154 

31 

32 

4 

170 

32 

33 

4 

185 

33 

34 

4 

200 

34 

35 

3 

215 

35 

36 

3 

230 

36 

37 

3 

245 

37 

38 

3 

260 

38 

39 

<;2 

275 

39 

40 

.0099052 

.0109291 

40 

41 

2 

306 

41 

42 

2 

321 

42 

43 

2 

336 

43 

44 

1 

352 

44 

45 

1 

367 

45 

46 

1 

382 

46 

47 

1 

397 

47 

48 

0 

413 

48 

49 

0 

428 

49 

50 

.0099050 

.0109443 

50 

51 

.0099050 

459 

51 

52 

.0099049 

474 

52 

53 

9 

489 

53 

54 

9 

505 

54 

55 

9 

520 

55 

56 

9 

535 

56 

57 

8 

551 

57 

58 

8 

566 

58 

- 59 

8 

582 

59 

60 

.0099048 

.0109597 

60 


P 

Interpolating Table , 


Tabular Differences. 


diff.P 


14 

15 

16 


tt 

4.3 

n 

4.0 

// 

3.75 

0 

1 

12.9 

12.0 

11.25 

o 

21.4 

20.0 

18.75 

u 

3 

30.0 

28.0 

26.25 

A 

38.6 

36.0 

33.75 


5 

47.1 

44.0 

41 25 

6 

55 7 

52.0 

48.75 

7 

64.3 

60.0 

56.25 

8 

72.9 

68.0 

63.75 

9 

81.4 

76 0 

71.25 

10 

on n 

qa 0 

78.75 

yu. u 

o'* . U 

11 

98.6 

92.0 

86.25 

12 

107.1 

100.0 

93.75 

13 

115.7 

108.0 

101.25 

14 


116.0 

108.75 


15 



116.25 



16 







8 





























































25 ° 


t 

Reciprocal 

M 

Reciprocal 

P 

0 

100.948 

92.002 

1 

8 

91.989 

2 

8 

.977 

3 

8 

.964 

4 

9 

.952 

5 

9 

.940 

6 

9 

.927 

7 

9 

.915 

8 

.949 

.902 

9 

.950 

.890 

10 

100.950 

91.877 

11 

0 

.865 

12 

0 

.852 

13 

1 

.840 

14 

1 

.827 

15 

1 

.815 

16 

1 

.802 

17 

2 

.790 

18 

2 

.777 

19 

2 

.765 

20 

100.952 

91.752 

21 

2 

.739 

22 

3 

.727 

23 

3 

.714 

24 

3 

.702 

25 

3 

.689 

26 

4 

.676 

27 

4 

.664 

28 

4 

.651 

29 

4 

.639 

• 

30 

100.955 

91.626 

31 

5 

.613 

32 

5 

.601 

33 

5 

.588 

34 

5 

.575 

35 

6 

.563 

36 

6 

.550 

37 

6 

.537 

38 

6 

.525 

39 

• 7 

.512 

40 

100.957 

91.499 

41 

7 

.486 

42 

7 

.474 

43 

8 

.461 

44 

8 

.448 

45 

8 

.435 

46 

8 

.423 

47 

8 

.410 

48 

9 

.397 

49 

9 

.384 

50 

100.959 

91.372 

51 

.959 

.359 

52 

.960 

.346 

53 

0 

.333 

54 

0 

.320 

55 

0 

.307 

56 

1 

.295 

57 

1 

.282 

58 

1 

.269 

59 

1 

.256 

60 

100.962 

91.243 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

12 

13 

ft 

5.0 

// 

4.6 

0 

1 

15.0 

13.8 

2 

25.0 

23.1 

3 

35.0 

32.3 

4 

45.0 

41.5 

5 

55.0 

50.8 

6 

65.0 

60.0 

7 

75.0 

69.2 

8 

85.0 

78.5 

9 

95.0 

87.7 

10 

105.0 

96.9 

11 

115.0 

106.2 

12 


115.4 

13 





Log. M 

Log. P 

/ 

7.9959039 

8.0362040 

0 

29 

2626 

1 

20 

3212 

2 

10 

3799 

3 

.9959000 

4387 

4 

.9958990 

4975 

5 

80 

5562 

6 

70 

6151 

7 

60 

6741 

8 

51 

7330 

9 

7.9958941 

8.0367920 

10 

31 

8511 

11 

21 

9102 

12 

11 

.0369693 

13 

.9958901 

.0370285 

14 

.9958891 

0878 

15 

81 

1470 

16 

71 

2063 

17 

62 

2657 

18 

52 

3251 

19 

7.9958842 

8.0373845 

20 

32 

4441 

21 

22 

5035 

22 

12 

5632 

23 

.9958802 

6228 

24 

.9958792 

6824 

25 

82 

7422 

26 

72 

8020 

27 

62 

8617 

28 

52 

9216 

29 

7.9958742 

8.0379816 

30 

32 

.0380415 

31 

22 

1015 

32 

12 

1615 

33 

.9958702 

2215 

34 

.9958692 

2817 

35 

82 

3419 

36 

72 

4022 

37 

62 

4624 

38 

52 

5227 

39 

7.9958642 

8.0385831 

40 

32 

6434 

41 

22 

7039 

42 

12 

7643 

43 • 

.9958602 

8249 

44 

.9958592 

8855 

45 

82 

.0389460 

46 

72 

.0390067 

47 

62 

0675 

48 

51 

1282 

49 

7.9958541 

8.0391890 

50 

31 

2499 

51 

21 

3107 

52 

11 

3717 

53 

.9958501 

4327 

54 

.9958491 

4937 

55 

81 

5548 * 

56 

71 

6160 

57 

61 

6771 

58 

51 

7383 

59 

7.9958441 

8.0397995 

60 


9 





















































26 ° 


' 

M 

P 

/ 

0 

.0099048 

.0109597 

0 

1 

7 

613 

1 

2 

7 

628 

2 

3 

7 

644 

3 

4 

7 

659 

4 

5 

6 

675 

5 

6 

6 

690 

6 

7 

6 

706 

7 

8 

6 

721 

8 

9 

6 

737 

9 

10 

.0099045 

.0109753 

10 

11 

5 

768 

11 

12 

5 

. 784 

12 

13 

5 

799 

13 

14 

4 

815 

14 

15 

4 

831 

15 

16 

4 

846 

16 

17 

4 

862 

17 

18 

3 

878 

18 

19 

3 

893 

19 

20 

.0099043 

.0109909 

20 

21 

3 

925 

21 

22 

3 

941 

22 

23 

2 

957 

23 

24 

! 2 

972 

24 

25 

2 

.0109988 

25 

26 

2 

.0110004 

26 

27 

1 

020 

27 

28 

1 

036 

28 

29 

1 

051 

29 

30 

.0099041 

.0110067 

30 

31 

0 

083 

31 

32 

0 

099 

32 

33 

0 

115 

33 

34 

.0099040 

131 

34 

35 

.0099039 

147 

35 

36 

9 

163 

36 

37 

9 

179 

37 

38 

9 

195 

38 

39 

9 

211 

39 

40 

.0099038 

.0110227 

40 

41 

8 

243 

41 

42 

8 

259 

42 

43 

8 

275 

43 

44 

7 

291 

44 

45 

7 

307 

45 

46 

7 

323 

46 

47 

7 

339 

47 

48 

6 

355 

48 

49 

6 

371 

49 

50 

.0099036 

.0110388 

50 

51 

6 

404 

51 

52 

5 

420 

52 

53 

5 

436 

53 

54 

5 

452 

54 

55 

5 

469 

55 

56 

5 

485 

56 

57 

4 

501 

57 

58 

4 

517 

58 

59 

4 

534 

59 

60 

.0099034 

.0110550 

60 


P 

Interpolating Table. 


Tabular Differences. 

diff. P 

15 

16 

17 

// 

4.0 

n 

3.75 

n 

3.5 

0 

1 

12.0 

11.25 

10.6 

2 

20.0 

18.75 

17.6 

3 

28.0 

26.25 

24.7 

4 

36.0 

33.75 

31.8 

5 

44.0 

41.25 

38.8 

6 

52.0 

48.75 

45.9 

7 

60.0 

56.25 

52.9 

8 

68.0 

*63.75 

60.0 

9 

76.0 

71.25 

67.1 

10 

84.0 

78.75 

74.1 

11 

92.0 

86.25 

81.2 

12 

100.0 

93.75 

88.2 

13 

108.0 

101.25 

95.3 

14 

116.0 

108.75 

102,4 

15 


116.25 

109.4 

16" 




116.5 

17 







10 





























































26 ° 



Reciprocal 

M 

Reciprocal 

P 

0 

100.962 

91.243 

1 

2 

.230 

2 

2 

.217 

3 

2 

.205 

4 

2 

.192 

5 

3 

.179 

6 

3 

.166 

7 

3 

.153 

8 

3 

.140 

9 

4 

.127 

10 

100.964 

91.114 

11 

4 

.101 

12 

4 

.088 

13 

5 

.075 

14 

5 

.062 

15 

5 

.049 

16 

5 

.036 

17 

6 

.023 

18 

6 

91.010 

19 

6 

90.997 

20 

100.966 

90.984 

21 

7 

.971 

22 

7 

.958 

23 

7 

.945 

24 

7 

.932 

25 

7 

.919 

26 

8 

.906 

27 

8 

.893 

28 

8 

.880 

29 

8 

.867 

30 

100.969 

90.854 

31 

9 

.840 

32 

9 

.827 

33 

.969 

.814 

34 

.970 

.801 

35 

0 

.788 

36 

0 

.775 

37 

0 

.762 

38 

1 

.748 

39 

1 

.735 

40 

100.971 

90.722 

41 

1 

.709 

42 

2 

.696 

43 

2 

.682 

44 

2 

.669 

45 

2 

.656 

46 

2 

.643 

47 

3 

.630 

48 

3 

.616 

49 

3 

.603 

50 

100.973 

90.590 

51 

4 

.577 

52 

4 

.563 

53 

4 

.550 

54 

4 

.537 

55 

5 

.523 

56 

5 

.510 

57 

5 

.497 

58 

5 

.484 

59 

6 

.470 

60 

100.976 

90.457 


Reciprocal P 
Interpolating Table 


Tabular Differences. 

12 

13 

14 


// 

// 

5.0 

4.6 

4.3 

15.0 

13.8 

12.9 

25.0 

23.1 

21.4 

35.0 

32.3 

30.0 

45.0 

41.5 

38.6 

55.0 

50.8 

47.1 

65.0 

60.0 

55.7 

75.0 

69.2 

64.3 

85.0 

78.5 

72.9 

95.0 

87.7 

81.4 

105.0 

96.9 

90.0 

115.0 

106.2 

98.6 


115.4 

107.1 




115.7 







diff. 
rep. P 


0 

1 

2 

3 

4 

5 

6 

7 

8 
9 

10 

11 

12 

13 

14 


Log. M 

Log. P 

/ 

7.9958441 

8.0397995 

0 

30 

8609 

1 

20 

9222 

2 

10 

.0399836 

3 

.9958400 

.0400450 

4 

.9958390 

1065 

5 

80 

1680 

6 

70 

2296 

7 

59 

2912 

8 

49 

3529 

9 

7.9958339 

8.0404146 

10 

29 

4763 

11 

19 

5382 

12 

.9958309 

6000 

13 

.9958298 

6619 

14 

88 

7238 

15 

78 

7858 

16 

68 

8479 

17 

58 

9099 

18 

47 

.0409720 

19 

7.9958237 

8.0410342 

20 

27 

0964 

21 

17 

1587 

22 

.9958206 

2209 

23 

.9958196 

2833 

24 

86 

3457 

25 

76 

4081 

26 

66 

4707 

27 

55 

5331 

28 

45 

5958 

29 

7.995*8135 

8.0416583 

30 

25 

7210 

31 

14 

. 7838 

32 

.9958104 

8465 

33 

.9958094 

9093 

34 

83 

.0419721 

35 

73 

.0420351 

36 

63 

0979 

37 

53 

1610 

38 

42 

2241 

39 

7.9958032 

8.0422871 

40 

22 

3502 

41 

11 

4134 

42 

.9958001 

4766 

43 

.9957991 

5398 

44 

80 

6032 

45 

70 

6666 

46 

60 

7299 

47 

49 

7934 

48 

39 

8569 

49 

7.9957929 

8.0429204 

50 

. 18 

.0429840 

51 

.9957908 

.0430476 

52 

.9957898 

1113 

53 

87 

1750 

54 

77 

2388 

55 

67 

3026 

56 

56 

3665 

57 

46 

4304 

5a 

35 

4944 

59 

7.9957825 

8.0435583 

60 


11 


























































0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


27 ° 


M 

P 

f 

.0099034 

.0110550 

0 

3 

566 

1 

3 

582 

2 

3 

599 

3 

3 

615 

4 

2 

632 

5 

2 

648 

6 

2 

664 

7 

2 

681 

8 

1 

697 

9 

.0099031 

.0110714 

10 

1 

730 

11 

1 

747 

12 

1 

763 

13 

0 

779 

14 

0 

796 

15 

0 

812 

16 

.0099030 

829 

17 

.0099029 

846 

18 

9 

862 

19 

.0099029 

.0110879 

20 

9 

895 

21 

8 

912 

22 

8 

928 

23 

8 

945 

24 

8 

962 

25 

7 

978 

26 

7 

.0110995 

27 

7 

.0111012 

28 

7 

028 

29 

.0099026 

.0111045 

30 

6 

062 

31 

6 

079 

32 

6 

095 

33 

5 

112 

34 

5 

129 

35 

5 

146 

36 

5 

163 

37 

5 

179 

38 

4 

196 

39 

.0099024 

.0111213 

40 

4 

230 

41 

4 

247 

42 

3 

264 

43 

3 

218 

44 

3 

298 

45 

3 

315 

46 

2 

332 

47 

2 

349 

48 

2 

366 

49 

.0099022 

.0111383 

50 

1 

400 

51 

. 1 

417 

52 

1 

434 

53 

1 

451 

54 

0 

468 

55 

0 

485 

56 

0 

502 

57 

.0099020 

519 

58 

.0099019 

536 

59 

.0099019 

.0111554 

60 


P 


Interpolating Table. 


Tabular Differences. 

diff.P 

16 

17 

18 

ft 

3.75 

// 

3.5 

// 

3.3 

0 

1 

11.25 

10.6 

10.0 

2 

18.75 

17.6 

16.7 

3 

26.25 

24.7 

23.3 

4 

33.75 

31.8 

30.0 

5 

41.25 

38.8 

36.7 

6 

48.75 

45.9 

43.3 

7 

56.25 

52.9 

50.0 

8 

63.75 

60.0 

56.7 

9 

71.25 

67.1 

63.3 

10 

78.75 

74.1 

70.0 

11 

86.25 

81.2 

76.7 

12 

93.75 

88.2 

83.3 

13 

101.25 

95.3 

90.0 

14 

108.75 

102.4 

96.7 

15 

116.25 

109.4 

103.3 

16 


116.5 

110.0 

17 




116.7 

18 









12 



























































27 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

100.976 

90.457 

1 

6 

.444 

2 

6 

.430 

3 

7 

.417 

4 

7 

.404 

5 

7 

.390 

6 

7 

.377 

7 

8 

.363 

8 

8 

.350 

9 

8 

.337 

10 

100.978 

90.323 

11 

8 

.310 

12 

9 

.296 

13 

9 

.283 

14 

9 

.269 

15 

.979 

.256 

16 

.980 

.243 

17 

0 

.229 

18 

0 

.216 

19 

0 

.202 

20 

100.981 

90.189 

21 

1 

.175 

22 

1 

.162 

23 

1 

.148 

24 

2 

.135 

. 25 

2 

.121 

26 

2 

.108 

27 

2 

.094 

28 

3 

.081 

29 

3 

.067 

30 

100.983 

90.053 

31 

3 

.040 

32 

4 

.026 

33 

4 

90.013 

34 

4 

89.999 

35 

4 

.986 

36 

5 

.972 

37 

5 

.958 

38 

5 

.945 

39 

5 

.931 

40 

100.986 

89.917 

41 

6 

.904 

42 

6 

.890 

43 

6 

.876 

44 

7 

.863 

45 

7 

.849 

46 

7 

.835 

47 

7 

.822 

48 

8 

.808 

49 

8 

.794 

50 

100.988 

89.781 

51 

8 

.767 

52 

9 

.753 

53 

9 

.739 

54 

9 

.726 

55 

.989 

.712 

56 

.990 

.698 

57 

0 

.684 

58 

0 

.671 

59 

0 

.657 

60 

100.991 

89.643 


Reciprocal P 
Interpolating Table 


Tabular Diff. 

diff. 
rep. P 

13 

14 

// 

4.6 

// 

4.3 

0 

1 

13.8 

12.9 

o 

23.1 

21.4 

L 

Q 

32.3 

30.0 

O 

4 

41.5 

38.6 

K 

50.8 

47.1 

U 

6 

60.0 

55.7 

7 

69.2 

64.3 

i 

8 

78.5 

72.9 

9 

87.7 

81.4 

10 

Qfi Q 

on n 

yo. y 

yu. u 

11 

106.2 

98.6 

12 

115.4 

107.1 

13 


115.7 



14 




Log. M 

Log. P 

f 

7.9957825 

8.0435583 

0 

15 

6224 

1 

.9957804 

6864 

2 

.9957794 

7506 

3 

83 

8148 

4 

73 

8790 

5 

63 

.0439433 

6 

52 

.0440076 

7 

42 

0719 

8 

31 

1364 

9 

7.9957721 

8.0442009 

10 

11 

2654 

11 

.9957700 

3300 

12 

.9957690 

3945 

13 

79 

4592 

14 

69 

5239 

15 

58 

5887 

16 

48 

6534 

17 

37 

7183 

18 

27 

7831 

19 

7.9957616 

8.0448481* 

20 

.9957606 

9130 

21 

.9957595 

.0449781 

22 

85 

.0450431 

23 

74 

1082 

24 

64 

1733 

25 

53 

2386 

26 

43 

• 3038 

27 

32 

3691 

28 

22 

4344 

29 

7.9957511 

8.0454999 

30 

.9957501 

5653 

31 

.9957490 

6308 

32 

80 

6963 

33 

69 

7619 

34 

59 

8275 

35 

48 

8931 

36 

38 

.0459589 

37 

27 

.0460246 

38 

16 

0904 

39 

7.9957406 

8.0461563 

40 

.9957395 

2222 

41 

85 

2881 

42 

74 

3542 

43 

64 

4202 

44 

53 

4863 

45 

42 

5524 

46 

32 

6186 

47 

21 

6848 

48 

11 

7511 

49 

7.9957300 

8.0468174 

50 

.9957289 

8838 

51 

79 

.0469502 

52 

68 

.0470167 

53 

58 

0832 

54 

47 

1497 

55 

36 

2164 

56 

26 

2830 

57 

15 

3497 

58 

.9957204 

4164 

59 

7.9957194 

8.0474833 

60 


13 
























































28 


M 


0 

.0099019 

1 

9 

2 

9 

3 

8 

4 

8 

5 

8 

6 

8 

7 

7 

8 

7 

9 

7 

10 

.0099017 

11 

7 

12 

6 

13 

6 

14 

6 

15 

6 

16 

5 

17 

5 

18 

5 

19 

5 

20 

.0099014 

21 

4 

22 

4 

23 

4 

24 

3 

25 

3 

26 

3 

27 

3 

28 

2 

29 

2 

30 

.0099012 

31 

2 

32 

1 

33 

1 

34 

1 

35 

1 

36 

0 

37 

0 

38 

0 

39 

.0099010 

40 

.0099009 

41 

9 

42 

9 

43 

9 

44 

8 

45 

8 

46 

8 

47 

8 

48 

7 

49 

7 

50 

.0099007 

51 

7 

52 

6 

53 

6 

54 

6 

55 

6 

56 

5 

57 

5 

58 

5 

59 

5 

60 

.0099004 


P 

t 

.0111554 

0 

571 

1 

588 

2 

605 

3 

622 

4 

640 

5 

657 

6 

674 

7 

691 

8 

709 

9 

.0111726 

10 

743 

11 

761 

12 

778 

13 

795 

14 

813 

15 

830 

16 

847 

17 

865 

18 

882 

19 

.0111900 

20 

917 

21 

935 

22 

952 

23 

970 

24 

.0111987 

25 

.0112005 

26 

022 

27 

040 

28 

057 

29 

.0112075 

30 

093 

31 

110 

32 

128 

33 

146 

34 

163 

35 

181 

36 

199 

37 

216 

38 

234 

39 

.0112252 

40 

270 

41 

287 

42 

305 

43 

323 

44 

341 

45 

359 

46 

377 

47 

394 

48 

412 

49 

.0112430 

50 

448 

51 

466 

52 

484 

53 

502 

54 

520 

55 

538 

56 

556 

57 

' 574 

58 

592 

59 

.0112610 

60 


P 

Interpolating Table. 


Tabular Diff. 

diff. P 

17 

18 

3.5 

3.3 

0 

1 

10.6 

10.0 

2 

3 

17.6 

16.7 

24.7 

23.3 

4 

" ~ 

31.8 

30.0 


38.8 

36.7 

0 

6 

45.9 

43.3 

7 

52.9 

50.0 

8 

60.0 

56.7 

9 

67.1 

63.3 

10 

74.1 

70.0 

1 1 

81.2 

76.7 

I 1 

12 

88.2 

83.3 


95.3 

90.0 

lo 

14 

102.4 

96.7 

15 

109.4 

103.3 


116.5 

110.0 

10 

17 


116.7 


18 




14 


















































28 ° 


r 

Reciprocal 

M 

Reciprocal 

P 

0 

100.991 

89.643 

1 

1 

.629 

2 

1 

.615 

3 

1 

.602 

4 

2 

.588 

5 

2 

.574 

6 

2 

.560 

7 

2 

.546 

8 

3 

.533 

9 

3 

.519 

10 

100.993 

89.505 

11 

3 

.491 

12 

3 

.477 

13 

4 

.463 

14 

4 

449 

15 

4 

.435 

16 

. 4 

.421 

17 

5 

.408 

18 

5 

.394 

19 

5 

.380 

20 

100.995 

89.366 

21 

6 

.352 

22 

6 

.338 

23 

6 

.324 

24 

6 

.310 

25 

7 

.296 

' 26 

7 

.282 

27 

7 

.268 

28 

7 

.254 

29 

8 

.240 

30 

100.998 

89.226 

31 

8 

.212 

32 

8 

.198 

33 

9 

.184 

34 

9 

.170 

35 

9 

.156 

36 

100.999 

.142 

37 

101.000 

.128 

38 

0 

.114 

39 

0 

.099 

40 

101.000 

89.085 

41 

1 

.071 

42 

1 

.057 

43 

1 

.043 

44 

2 

.029 

45 

2 

.015 

46 

2 

89.001 

47 

2 

88.987 

48 

3 

.972 

49 

3 

.958 

56 

101.003 

88.944 

51 

3 

.930 

62 

4 

.916 

53 

4 

.902 

54 

4 

.887 

55 

4 

.873 

56 

5 

.859 

57 

5 

.845 

58 

5 

.830 

59 

5 

.816 

60 

101.006 

88.802 


Reciprocal P 
Interpolating Table. 


Tabular Differences. 

diff. 
rep. P 

13 

14 

15 

// 

4.6 

// 

4.3 

// 

4.0 

0 

1 

13.8 

12.9 

12.0 

2 

23.1 

21.4 

20.0 

3 

32.3 

30.0 

28.0 

4 

41.5 

38.6 

36.0 

5 

50.8 

47.1 

44.0 

6 

60.0 

55.7 

52.0 

7 

AQ 0 

64.3 

60.0 

oy. l 

8 

78.5 

72.9 

68.0 

9 

87.7 

81.4 

76.0 

10 

96.9 

90.0 

84.0 

11 

106.2 

98.6 

92.0 

12 

115.4 

107.1 

100.0 

13 


115.7 

108.0 

14 

15 




116.0 







Log. M 

Log. P 

f 

7.9957194 

8.0474833 

0 

83 

5501 

1 

72 

6170 

2 

62 

6839 

3 

51 

7509 

4 

40 

8179 

5 

30 

8850 

6 

19 

.0479521 

7 

.9957108 

.0480193 

8 

.9957098 

0865 

9 

7.9957087 

8.0481537 

10 

76 

2211 

11 

66 

2884 

12 

55 

3559 

13 

44 

4233 

14 

33 

4908 

15 

23 

5584 

16 

12 

6259 

17 

.9957001 

6936 

18 

.9956991 

7613 

19 

7.9956980 

8.0488289 

20 

69 

8968 

21 

58 

.0489646 

22 

48 

.0490325 

23 

37 

1004 

24 

26 

1684 

25 

15 

2364 

26 

.9956905 

3044 

27 

.9956894 

3726 

28 

83 

4407 

29 

7.9956872 

8.0495090 

30 

62 

5772 

31 

51 

6455 

32 

40 

7139 

33 

' 29 

7822 

34 

19 

8508 

35 

.9956808 

9192 

36 

.9956797 

.0499878 

37 

86 

.0500564 

38 

75 

1250 

39 

7.9956765 

8.0501937 

40 

54 

2624 

41 

43 

3311 

42 

32 

4000 

43 

21 

4689 

44 

10 

5378 

45 

.9956700 

6068 

46 

.9956689 

6758 

47 

78 

7449 

48 

67 

8140 

49 

7.9956656 

8.0508832 

50 

45 

.0509523 

51 

34 

.0510216 

52 

24 

0909 

53 

13 

1602 

54 

.9956602 

2296 

55 

.9956591 

2991 

56 

80 

3686 

57 

69 

4382 

58 

58 

5077 

59 

7.9956547 

8.0515773 

60 


15 























































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


29 ° 


M 

P 

/ 

.0099004 

.0112610 

0 

4 

628 

1 

4 

646 

2 

4 

664 

3 

3 

682 

4 

3 

701 

5 

3 

719 

6 

3 

737 

7 

2 

755 

8 

2 

773 

9 

.0099002 

.0112792 

10 

2 

810 

11 

1 

828 

12 

1 

846 

13 

1 

864 

14 

1 

883 

15 

0 

901 

16 

0 

919 

17 

0 

938 

18 

.0099000 

956 

19 

.0098999 

.0112974 

20 

9 

.0112993 

21 

9 

.0113011 

22 

9 

030 

23 

8 

048 

24 

8' 

067 

25 

8 

085 

26 

8 

103 

27 

7 

122 

28 

7 

140 

29 

.0098997 

.0113159 

30 

7 

177 

31 

6 

196 

32 

6 

215 

33 

6 

233 

34 

6 

252 

35 

5 

270 

36 

5 

289 

37 

5 

308 

38 

5 

326 

39 

.0098994 

.0113345 

40 

4 

364 

41 

4 

382 

42 

4 

401 

43 

3 

420 

44 

3 

439 

45 

3 

457 

46 

3 

476 

47 

2 

495 

48 

2 

514 

49 

.0098992 

.0113533 

50 

' 2 

551 

51 

1 

570 

52 

1 

589 

. 53 

1 

608 

54 

1 

627 

55 

0 

646 

56 

0 

• 665 

57 

0 

684 

58 

.0098990 

703 

59 

.0098989 

.0113722 

60 


P 

Interpolating Table. 


Tabular Diff. 

diff. P 

18 

19 

// 

3.3 

// 

3.2 

0 

1 

10.0 

9.5 

2 

16.7 

15.8 

3 

23.3 

22.1 

4 

30.0 

28.4 

5 

36.7 

34.7 

6 

43.3 

41.1 

7 

50.0 

47.4 

8 

56.7 

53.7 

9 

63.3 

60.0 

10 

70.0 

66.3 

11 

76.7 

72.6 

12 

83.3 

78.9 

13 

90.0 

85.3 

14 

96.7 

91.6 

15 

103.3 

97.9 

16 

110.0 

104.2 

17 

116.7 

110.5 

18 


116.8 

19 





16 

























































29 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 




Log. M 

Log. P 

f 

0 

101.006 

88.802 v'' 




7.9956547 

8.0515773 

0 

1 

6 

.788 




36 

6471 

1 

2 

6 

.773 




26 

7168 

2 

3 

6 

.759 




15 

7865 

3 

4 

7 

.745 




.9956504 

8564 

4 

5 

7 

.731 




.9956493 

9263 

5 

6 . 

7 

.716 




82 

.0519962 

6 

7 

7 

.702 




71 

.0520662 

7 

8 

8 

.688 




60 

1362 

8 

9 

8 

.673 




49 

2063 

9 

10 

101.008 

88.659 




7.9956438 

8.0522764 

10 

11 

8 

.645 




27 

3465 

11 

12 

9 

.631 




16 

4168 

12 

13 

9 

.616 




.9956405 

4871 

13 

14 

9 

.602 




.9956394 

5573 

14 

15 

.009 

.587 




84 

6278 

15 

16 

.010 

.573 

Reciprocal P 

73 

6981 

16 

17 

0 

.559 

Interpolating Table. 

62 

7685 

17 

18 

0 

.544 




51 

8391 

18 

19 

0 

.530 

Tabular Diff. 

diff. 

40 

9096 

19 






rep. P 




20 

101.011 

88.516 

14 

15 


7.9956329 

8.0529802 

20 

21 

1 

.501 

// 

// 

A 

18 

.0530509 

21 

22 

1 

.487 

4.3 

4.0 

U 

.9956307 

1216 

22 

23 

1 

.472 



1 

.9956296 

1923 

23 

24 

2 

.458 

12.9 

12.0 

o 

85 

2631 

24 




21.4 

20 0 

L 




. 25 

2 

.444 



3 

74 

3340 

25 

26 

2 

.429 

30.0 

28 0 

A 

63 

4048 

26 

27 

2 

.415 

38.6 

36.0 

4: 

52 

4758 

27 

28 

3 

.400 



5 

41 

5468 

28 

29 

3 

.386 

47.1 

44.0 


30 

6178 

29 




55.7 

52 0 

0 




30 

101.013 

88.371 



7 

7.9956219 

8.0536889 

30 

31 

3 

.357 

64.3 

60.0 

c 

.9956208 

7600 

31 

32 

4 

.342 

72.9 

68.0 

o 

.9956197 

8312 

32 

33 

4 

.328 



9 

86 

9025 

33 

34 

4 

.313 

81.4 

76.0 

10 

75 

.0539737 

34 




90.0 

84.0 




35 

4 

.299 



11 

64 

.0540450 

35 

36 

5 

.284 

98.6 

92.0 

12 

53 

1164 

36 

37 

5 

.270 

107.1 

100.0 

42 

1878 

37 

38 

5 

.255 



13 

31 

2593 

38 

39 

6 

.241 

115.7 

108.0 

14. 

19 

3309 

39 





116.0 

14 




40 

101.016 

88.226 



15 

7.9956108 

8.0544024 

40 

41 

6 

.212 




.9956097 

4740 

41 

42 

6 

.197 




86 

5457 

42 

43 

7 

.183 




75 

6174 

43 

44 

7 

.168 




64 

6891 

44 

45 

7 

.153 




53 

7610 

45 

46 

7 

.139 




42 

8328 

46 

47 

8 

.124 




31 

9047 

47 

48 

8 

.110 




20' 

.0549767 

48 

49 

8 

.095 




.9956009 

.0550487 

49 

50 

101.018 

88.080 




7.9955998 

8.0551207 

50 

51 

9 

.066 




87 

1928 

51 

52 

9 

.051 




76 

2650 

52 

53 

9 

.037 




64 

3372 

53 

54 

.019 

.022 




53 

4094 

54 

55 

.020 

88.007 




42 

4818 

55 

56 

0 

87.993 




31 

5541 

56 

57 

0 

.978 




20 

6265 

57 

58 

0 

.963 




.9955909 

6990 

58 

59 

1 

.949 




.9955898 

7715 

59 

60 

101.021 

87.934 




7.9955887 

8.0558440 

60 


17 



















































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


30 ° 


M 

P 

/ 

.0098989 

.0113722 

0 

9 

741 

1 

9 

760 

2 

9 

779 

3 

8 

798 

4 

8 

817 

5 

8 

836 

6 

8 

855 

7 

7 

874 

8 

7 

894 

9 

.0098987 

.0113913 

10 

7 

932 

11 

6 

951 

12 

6 

970 

13 

6 

.0113989 

14 

6 

.0114009 

15 

5 

028 

16 

5 

047 

17 

5 

066 

18 

5 

086 

19 

.0098984 

.0114105 

20 

4 

124 

21 

4 

144 

22 

4 

163 

23 

3 

183 

24 

3 

202 

25 

3 

221 

26 

3 

241 

27 

2 

260 

28 

2 

280 

29 

.0098982 

.0114299 

30 

2 

319 

31 

1 

338 

32 

1 

358 

33 

1 

377 

34 

0 

397 

35 

0 

416 

36 

0 

436 

37 

.0098980 

456 

38 

.0098979 

475 

39 

.0098979 

.0114495 

40 

9 

515 

41 

9 

534 

42 

8 

554 

43 

8 

574 

44 

8 

593 

45 

8 

613 

46 

7 

633 

47 

7 

653 

48 

7 

672 

49 

.0098977 

.0114692 

50 

6 

712 

51 

6 

732 

52 

6 

752 

53 

6 

772 

54 

5 

791 

55 

5 

811 

56 

5 

831 

57 

5 

851 

58 

4 

871 

59 

.0098974 

.0114891 

60 



P 

Interpolating Table. 


Tabular Diff. 

diff.P 

19 

20 

n 

3.2 

// 

3.0 

0 

1 

9.5 

9.0 

2 

15.8 

15.0 

3 

22.1 

21.0 

.4 

28.4 

27.0 

5 

34.7 

33.0 

6 

41,1 

39.0 

7 

47.4 

45.0 

8 

53.7 

51.0 

9 

60.0 

57.0 

10 

66.3 

63.0 

11 

72.6 

69.0 

12 

78.9 

75.0 

13 

85.3 

81.0 

14 

91.6 

87.0 

15 

97.9 

93.0 

16 

104.2 

99.0 

17 

110.5 

105.0 

18 

116.8 

111.0 

19 


117.0 


20 





18 




























































30 ° 


y 

Reciprocal 

Reciprocal 




Log. M 

Log. P 

/ 


M 

P 






0 

101.021 

87.934 




7.9955887 

8.0558440 

0 

l 

1 

.919 




76 

9165 

1 

2 

1 

.904 




64 

.0559892 

2 

3 

2 

.890 




53 

.0560619 

3 

4 

2 

.875 




42 

1346 

4 

5 

2 

.860 




31 

2074 

5 

6 

2 

.846 




20 

2803 

6 

7 

3 

.831 




.9955809 

3531 

7 

8 

3 

.816 




.9955798 

4260 

8 

9 

3 

.801 




86 

4991 

9 

10 

101.024 

87.787 




7.9955775 

8.0565721 

10 

11 

4 

.772 




64 

6451 

11 

12 

4 

.757 




53 

7182 

12 

13 

4 

.742 




42 

7915 

13 

14 

5 

.727 




31 

8647 

14 

15 

5 

.713 




19 

.0569379 

15 

16 

5 

.698 

Reciprocal I 

> 

.9955708 

.0570113 

16 

17 

5 

.683 

Interpolating Table. 

.9955697 

0847 

17 

18 

19 

6 

.668 

.653 




86 

75 

1581 

18 

6 

Tabular Diff. 

diff. 

2315 

19 






rep. P 











20 

21 

20 

101.026 

87.638 

14 

15 

7.9955663 

8.0573051 

21 

6 

.624 

n 

,, 

0 

52 

3787 

22 

23 

7 

7 

.609 

.594 

4.3 

4.0 

41 

30 

4523 

5259 

22 

23 

1 

12.9 

12.0 

24 

7 

.579 

o 

19 

5997 

24 




21.4 

20.0 

A 




25 

7 

.564 

3 . 

.9955607 

6735 

25 



30.0 

28.0 

26 

8 

.549 


.9955596 

7472 

26 

4 

27 

28 

8 

8 

.534 

.520 

38.6 

36.0 

5 

85 

74 

8212 

8951 

27 

28 

47.1 

44.0 

29 

8 

.505 

6 

62 

.0579690 

29 

30 

101.029 

87.490 

55.7 

52.0 

A 

7.9955551 

1 

I 8.0580430 

30 

7 

64.3 

60.0 

31 


.475 


40 

1171 

31 

9 

8 

32 

33 

.029 

.030 

.460 

.445 

72.9 

68.0 

29 

17 

. 1912 
2654 

32 

33 

9 

81.4 

76.0 

34 

0 

.430 


.9955506 

3396 

34 

10 

35 

0 

.415 

90.0 

84.0 

.9955495 

4138 

35 

11 



36 

0 

.400 

98.6 

92.0 

12 

84 

4882 

86 

37 

1 

.385 

107.1 

inn n 

72 

5625 

37 

38 

1 

.370 

1UU .u 

13 

61 

6369 

38 



39 

1 

.355 

115.7 

108 0 

14 

50 

7114 

39 





116.0 




40 

101.031 

87.340 


15 

7.9955439 

8.0587859 

40 

■ 


41 

2 

.325 




27 

8605 

41 

42 

2 

.310 




16 

.0589351 

42 

43 

2 

.295 




.9955405 

.0590097 

43 

44 

2 

.280 




.9955393 

0845 

44 

45 

3 

.265 




82 

1592 

45 

46 

3 

.250 




71 

2340 

46 

47 

3 

.235 




60 

3088 

47 

48 

3 

.220 




48 

3838 

48 

49 

4 

.205 

1 



37 

4587 

49 

50 

101.034 

87.190 




7.9955326 

8.0595337 

50 

51 

4 

.175 




14 

6088 

51 

52 

4 

.160 




.9955303 

6839 

52 

53 

5 

.145 




.9955292 

7591 

53 

54 

5 

.130 




80 

8343 

54 

55 

5 

.115 



, 

69 

9095 

55 

56 

6' 

.099 




58 

.0599848 

56 

57 

6 

.084 




46 

.0600602 

57 

58 

6 

.069 


, 


35 

1356 

58 

59 

6 

.054 




24 

2110 

59 

60 

101.037 

87.039 




7.9955212 

8.0602865 

60 


19 


























































31 ° 


/ 

M 

P 

t 

0 

.0098974 

.0114891 

0 

1 

4 

911 

1 

2 

4 

931 

2 

3 

3 

951 

3 

4 

3 

971 

4 

5 

3 

.0114991 

5 

6 

2 

.0115011 

6 

7 

2 

031 

7 

8 

2 

052 

8 

9 

2 

072 

9 

10 

.0098971 

.0115092 

10 

11 

1 

112 

11 

12 

1 

132 

12 

13 

1 

152 

13 

14 

0 

172 

14 

15 

0 

193 

15 

16 

0 

213 

16 

17 

.0098970 

233 

17 

18 

.0098969 

254 

18 

19 

9 

274 

19 

20 

.0098969 

.0115294 

20 

21 

9 

314 

21 

22 

8 

335 

22 

23 

8 

355 

23 

24 

8 

376 

24 

25 

8 

396 

25 

26 

7 

416 

26 

27 

7 

437 

27 

28 

7 

457 

28 

29 

7 

478 

29 

30 

.0098966 

.0115498 

30 

31 

6 

519 

31 

32 

6 

539 

32 

33 

5 

560 

33 

34 

5 

580 

34 

35 

5 

601 

35 

36 

5 

621 

36 

37 

4 

642 

37 

38 

4 

663 

38 

39 

4 

683 

39 

40 

.0098964 

.0115704 

40 

41 

3 

724 

41 

42 

3 

745 

42 

43 

3 

766 

43 

44 

3 

787 

44 

45 

2 

807 

45 

46, 

2 

828 

46 

47 

2 

849 

47 

48 

2 

870 

48 

49 

1 

890 

49 

50 

.0098961 

.0115911 

50 

51 

1 

932 

51 

52 

0 

953 

52 

53 

0 

974 

53 

54 

0 

.0115995 

54 

55 

.0098960 

.0116016 

55 

56 

.0098959 

037 

56 

57 

9 

058 

57 

58 

9 

078 

58 

59 

9 

099 

59 

60 

.0098958 

.0116120 

60 


P 

Interpolating Table. 


Tabular Diff. 

diff. P 

20 

21 

n 

3.0 

it 

2.9 

0 

1 

9.0 

8.6 

2 

15.0 

14.3 

3 

21.0 

20.0 

4 

27.0 

25.7 * 

5 

33.0 

31.4 

6 

39.0 

37.1 

7 

45.0 

42.9 

8 

51.0 

48.6 

9 

57.0 

54.3. 

10 

63.0 

60.0 

11 

69.0 

65.7 

12 

75.0 

71.4 

13 

81.0 

77.1 

14 

87.0 

82.9 

15 

93.0 

88.6 

16 

99.0 

94.3 

17 

105.0 

100.0 

18 

111.0 

105.7 

19 

117.0 

111.4 

20 


117.1 

21 





20 





































































31 ° 


t 

Reciprocal 

Reciprocal 




Log. M 

Log. P 

t 


M 

P 







0 

101.037 

87.039 




7.9955212 

8.0602865 

0 

1 

7 

.024 




.9955201 

3621 

1 

2 

7 

87.009 




.9955190 

4377 

2 

3 

7 

86.993 




78 

5134 

3 

4 

8 

.978 




67 

5890 

4 

5 

8 

.963 




56 

6648 

5 

6 

8 

.948 




44 

7407 

6 

7 

8 

.933 




33 

.8165 

7 

8 

9 

.918 




22 

8924 

8 

9 

9 

.902 




.9955110 

.0609683 

9 

10 

101.039 

86.887 




7.9955099 

8.0610443 

10 

11 

.040 

.872 




87 

1204 

11 

12 

0 

.857 




76 

1965 

12 

13 

0 

.842 




65 

2726 

13 

14 

0 

.826 




53 

3488 

14 

15 

1 

.811 




42 

4251 

15 

16 

17 

1 

1 

.796 

.781 

Reciprocal * 

Interpolating Table. 

30 

19 

5014 

5778 

16 

17 

18 

1 

.765 



' 

.9955008 

6542 

18 

19 

2 

.750 

Tabular Diff. 

diff. 

.9954996 

7306 

19 










20 

101.042 

86.735 

15 

16 

rep. J 

7.9954985 

8.0618071 

20 




21 

2 

.719 

" 

n 

0 

73 

8837 

21 

22 

2 

.704 

4.0 

3.75 

1 

62 

.0619603. 

22 

23 

3 

.689 

12.0 

11.25 

51 

.0620369 

23 

24 

3 

.674 



o 

39 

1136 

24 

20 0 

18.75 

& 

3 



25 

3 

.658 

28.0 

26.25 

28' 

1904 

25 

26 


.643 



A 

16 

2673 

26 

4 

36.0 

33.75 

i ± 

27 

4 

.628 

5 

.9954905 

3441 

27 

28 

29 

4 

.612 

.597 

44.0 

41.25 

.9954893 

82 

4210 

4979 

28 

29 

6 

4 




52 0 

48.75 

7 




30 

31 

101.045 

5 

86.582 
.566 

60.0 

56.25 

7.9954871 

59 

8.0625749 

6521 

30 

31 

8 

68.0 

63.75 

32 

5 

.551 

9 

48 

7291 

32 

33 

34 

5 

6 

.535 

.520 

76 0 

71.25 

36 

25 

8063 

8835 

33 

34 

10 

84.0 

78.75 


1 1 




35 

36 

6 

n 

.505- 

.489 

92.0 

86.25 

11 

1 9 

13 

.9954802 

.0629607 

.0630380 

35 

36 

O 

100.0 

93.75 

1- 

37 

6 

.474 

13 

.9954790 

1155 

37 

38 

39 

7 

7 

.458 

.443 

108.0 

101.25 

79 

67 

1929 

2703 

38 

39 

1 A 

116 0 

108.75 

Itc 

15 






40 

41 

101.047 

86.428 

.412 


116.25 

7.9954756 

8.0633478 

40 

8 


16 

44 

4253 

41 



42 

43 

8 

8 

.397 

.381 




33 

5029 

42 




21 

5807 

43 

44 

8 

.366 


• 


.9954710 

6584 

44 

45 

9 

.350 




.9954698 

7361 

45 

46 

9 

.335 




87 

8139 

46 

47 

9 

.319 




75 

8918 

47 

48 

.049 

.304 




64 

.0639698 

48 

. 49 

.050 

.288 




52 

.0640478 

49 

50 

101.050 

86.273 




7.9954641 

8.0641258 

50 

51 

0 

.257 




29 

2038 

51 

52 

0 

.242 




18 

2819 

52 

53 

1 

.226 




.9954606 

3601 

53 

54 

1 

.211 




.9954595 

4383 

54 

55 

1 

.195 




83 

5167 

55 

56 

2 

.180 




72 

5950 

56 

57 

2 

.164 




60 

6733 

57 

58 

2 

.149 




49 

7517 

58 

59 

2 

.133 




37 

8302 

59 

60 

101.053 

86.117 




7.9954526 

8.0649087 

60 


21 






























































f 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


32 ° 


M 

P 

/ 





.0098958 

.0116120 

0 


t 



8 

141 

1 





8 

163 

2 





8 

184 

3 





7 

205 

4 





7 

226 

5 





7 

247 

6 





7 

268 

7 





6 

289 

8 





6 

310 

9 





.0098956 

.0116331 

10 





5 

353 

11 


F 

1 


5 

374 

12 

Interpolating Table. 


5 

395 

13 









5 

416 

14 

Tabular Differences. 








diff. P 







4 

437 

15 

21 

22 

23 


4 

459 

16 

// 

// 

n 

0 

A 

A Qfi 

i n 

2.9 

o 7 

2.6 


4 

501 

1 1 

18 


1 

4 

8.6 

8.2 

7.8 

3 

523 

19 


2 


14.3 

13.6 

13.0 




.0098953 

.0116544 

20 

3 

20.0 

19.1 

18.3 

3 

565 

587 

21 

22 

A 

3 

25.7 

24.5 

23.5 

‘t 

rv 

2 

608 

23 

31.4 

30.0 

28.7 

0 

2 

630 

24 

6 


37.1 

35.5 

33.9 


651 

25 

7 

2 

42.9 

40.9 

39.1 

i 

2 

673 

26 

27 

8 

1 

694 

48.6 

46.4 

44.3 

9 


715 

28 




1 

54.3 

51.8 

49.6 

1 

737 

29 

10 

-.0098950 

60.0 

57.3 

54.8 

.0116758 

30 

11 

65.7 

62.7 

60.0 

0 

780 

31 

12 

0 

802 

32 

71.4 

68.2 

65.2 

13 

.0098950 

823 

33 




77.1 

73.6 

70.4 

.0098949 

845 

34 

14 

82.9 

79.1 

75.7 

A 

866 

35 

15 




9 

88.6 

84.5 

80.9 

9 

888 

36 

1 ft 

q 

910 

931 

37 

38 

94.3 

90.0 

86.1 

10 

8 

17 

100.0 

95.5 

91.3 

. 8 

953 

39 





105.7 

100.9 

96.5 

lo 

.0098948 

.0116975 

40 

1 0 

111.4 

106.4 

101.7 

iy 

8 

.0116996 

41 

on 

7 

.0117018 

42 

117.1 

111.8 

107.0 


n 

01 

040 

43 




7 


117.3 

112.2 

ZL 

062 

44 

7 


22 


.. 




117.4 

6 

084 

45 



23 




6 

105 

127 

46 

47 





6 





6 

149 

48 





5 

171 

49 





.0098945 

.0117193 

50 





5 

215 

51 





5 

237 

52 





4 

258 

53 





4 

280 

54 





4 

302 

55 





4 

324 

56 





3 

346 

57 





3 

368 

58 





3 

390 

59 





.0098942 

.0117413 

60 






22 





































































32 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 




Log. M 

Log. P 

/ 

0 

101.053 

86.117 




7.9954526 

8.0649087 

0 

1 

3 

.102 




14 

.0649874 

1 

2 

3 

.086 




.9954502 

.0650660 

2 

3 

3 

.071 




.9954491 

1447 

3 

4 

4 

.055 




79 

2234 * 

4 

5 

4 

.039 




68 

3022 

5 

6 

4 

.024 




56 

3810 

6 

7 

4 

86.008 




45 

4599 

7 

8 

5 

85.993 




33 

5389 

8 

9 

5 

.977 




21 

6179 

9 

10 

101.055 

85.961 




7.9954410 

8.0656969 

10 

11 

6 

.946 




.9954398 

7760 

11 

12 

6 

.930 




87 

8551 

12 

13 

6 

.914 




75 

.0659343 

13 

14 

6 

.899 




63 

.0660135 

14 

15 

16 

17 

18 

7 

7 

7 

.883 

.867 

.852 

Reciprocal P 

Interpolating Table. 

52 

40 

29 

0928 

1722 

2516 

15 

16 

17 

7 

.836 




17 

3310 

18 

19 

8 

.820 

Tabular Diff. 

.diff. 
rep. P 

.9954305 

4105 

19 

20 

101.058 

85.804 

15 

16 

7.9954294 

8.0664901 

20 





21 

8 

.789 

// 

tt 

0 

82 

5697 

21 

22 

9 

.773 

4 0. 

3.75 

1 

71 

6493 

22 

23 

9 

.757 

.742 

12.0 

11.25 

59 

47 

7291 

8088 

23 

24 

24 

9 

2 

20.0 

18.75 




Q 

- 25 

.059 

.726 

28.0 

26.25 

6 

36 

8886 

25 

26 

.060 

.710 



A 

24 

.0669685 

26 

36.0 

33.75 


27 

0 

.694 

K 

12 

.0670484 

27 

28 

. . 0 

.678 

44.0 

41.25 

0 

.9954201 

1283 

28 

ft 

29 

0 

.663 



.9954189 

2084 

29 

52.0 

48.75 

0 

7 




30 

31 

101.061 

1 

85.647 

.631 

60.0 

56.25 

7.9954178 

66 

8.0672884 

3686 

30 

31 

8 

68.0 

63.75 

32 

1 

.615 

9 

54 

4488 

32 

33 

34 

1 

.599 

.584 

76.0 

71.25 

43 

31 

5290 

6092 

33 

34 

2 

in 

84 0 

78.75 

IU 







11 




35 

36 

2 

2 

.568 

.552 

92.0 

86.25 

11 

12 

19 

.9954108 

6896 

7699 

35 

36 

100.0 

93.75 

37 

3 

.536 

13 

.9954096 

8503 

37 

38 

39 

3 

3 

.520 

.504 

108.0 

101.25 

84 

73 

.0679308 

.0680113 

38 

39 

1 A 

116.0 

108.75 

li 

15 



40 

101.063 

85.489 

.473 


116.25 

7.9954061 

8.0680920 

40 

41 

4 


16 

49 

1726 

41 

. 


42 

43 

4 

.457 

.441 




37 

26 

2533 

3340 

42 

43 

4 




44 

4 

.425 




14 

4148 

44 

45 

5 

.409 




.9954002 

4957 

45 

46 

5 

.393 


, 


.9953991 

5765 

46 

47 

5 

.377 




79 

6575 

47 

48 

6 

.361 




67 

7385 

48 

49 

6 

-.345 




56 

8195 

49 

50 

101.066 

85.330 




7.9953944 

8.0689006 

50 

51 

6 

.314 




32 

.0689818 

51 

52 

7 

.298 




21 

.0690630 

52 

53 

7 

.282 




.9953909 

1443 

53 

54 

7 

.266 




.9953897 

2256 

54 

55 

7 

.250 




85 

3069 

55 

56 

8 

.234 




74 

3884 

56 

57 

8 

.218 




62 

4698 

57 

58 

8 

.202 




50 

5513 

58 

59 

9 

.186 




38 

6329 

59 

60 

101.069 

85.170 




7.9953827 

8.0697145 

60 


23 



































































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


33 ° 


M 

P 

/ 

.0098942 

.0117413 

0 

2 

435 

1 

2 

457 

,2 

2 

479 

3 

1 

501 

4 

1 

523 

5 

1 

545 

6 

1 

568 

7 

0 

590 

8 

0 

612 

9 

.0098940 

.0117634 

10 

.0098940 

656 

11 

.0098939 

679 

12 

9 

701 

13 

9 

723 

14 

8 

746 

15 

8 

768 

16 

8 

790 

17 

8 

813 

18 

7 

835 

19 

.0098937 

.0117858 

20 

7 

880 

21 

7 

903 

22 

6 

925 

23 

6 

948 

24 

6 

970 

25 

5 

.0117993 

26 

5 

.0118015 

27 

5 

038 

28 

5 

060 

29 

.0098934 

.0118083 

30 

4 

106 

31 

4 

128 

32 

4 

151 

33 

3 

174 

34 

3 

196 

35 

3 

219 

36 

3 

242 

37 

2 

265 

38 

2 

287 

39 

.0098932 

.0118310 

40 

1 

333 

41 

1 

356 

42 

1 

379 

43 

1 

402 

44 

0 

425 

45 

0 

447 

46 

0 

470 

47 

.0098930 

493 

48 

.0098929 

516 

49 

.0098929 

.0118539 

50 

9 

562 

51 

8 

585 

52 

8 

608 

53 

8 

632 

54 

8 

655 

55 

7 

678 

56 

7 

701 

57 

7 

724 

58 

7 

747 

59 

.0098926 

.0118770 

60 


P 

Interpolating Table. 


Tabular Differences. 

diff. P 

22 

23 

24 

// 

2.7 

tt 

2.6 ' 

h 

2.5 

0 

1 

8.2 

7.8 

7.5 

2 

13.6 

13.0 

12.5 

3 

19.1 

18.3 

17.5 

4 

24.5 

23.5 

22.5 

5 

30.0 

28.7 

27.5- 

6 

35.5 

33.9 

32.5 

7 

40.9 

39.1 

37.5 

8 

46.4 

44.3 

42.5 

9 

51.8 

49.6 

47.5 

10 

57.3 

54.8 

52.5 

11 

62.7 

60.0 

57.5 

12 

68.2 

65.2 

62.5 

13 

73.6 

70.4 

67.5 

14 

79.1 

75.7 

72.5 

15 

84.5 

80.9 

77.5 

16 

90.0 

86.1 

82.5 

17 

95.5 

91.3 

87.5 

18 

100.9 

96.5 

92.5 

19 

106.4 

101.7 

97.5 

to 

o 

111.8 

107.0 

102.5 

21 

117.3 

112.2 

107.5 

22 


117.4 

112.5 

23 




117.5 

24 











































































33 ° 


/ 

Reciprocal 

Reciprocal 




Log. M 

Log. P 

/ 


M 

P 






0 

101.069 

85.170 




7.9953827 

8.0697145 

0 

1 

9 

.154 




15 

7962 

1 

2 

.069 

.138 




.9953803 

8780 

2 

3 

.070 

.122 




.9953791 

.0699598 

3 

4 

0 

.106 




80 

.0700416 

4 

5 

0 

.090 




68 

1235 

5 

6 

0 

.074 




56 

2054 

6 

7 

1 

.057 




44 

2874 

7 

8 

1 

.041 




33 

3694 

8 

9 

1 

.025 




21 

4515 

9 

10 

101.072 

85.009 




7.9953709 

8.0705336 

10 

11 

2 

84.993 




.9953697 

6158 

11 

12 

2 

.977 




86 

6980 

12 

13 

2 

.961 




74 

7804 

13 

14 

3 

.945 




62 

8628 

14 

15 

16 

3 

3 

.929 

.913 

Reciprocal P 

Interpolating Table. 

50 

38 

.0709452 

.0710276 

15 

16 

17 

3 

. .897 




27 

1102 

17 

18 

4 

.880 

Tabular Diff. 

diff. 

vstn P 

15 

1927 

18 

19 

4 

.864 

16 

17 

rep. r 

.9953603 

2753 

19 

20 

101.074 

84.848 

// 

// 

0 

7.9953591 

8.0713580 

20 

21 

5 

.832 

3.75 

3.5 

1 

79 

4407 

21 

22 

23 

5 

.816 

.800 

11.25 

10.6 

68 

56 

5235 

6063 

22 

5 

o 

23 

18.75 

17.6 

L 

24 

5 

.783 

3 

44 

6892 

24 

25 

6 

26.25 

24.7 

32 

7721 

25 

.767 

4 

33.75 

31.8 

26 

6 

.751 

C 

20 

8551 

26 

27 

28 

6 

rr 

.735 

.719 

41.25 

38.8 

0 

6 

.9953509 

.9953497 

.0719381 

.0720212 

27 

28 

7 

48.75 

45.9 

29 

7 

.702 

7 

85 

1044 

29 




cO Q 




30 

101.077 

84.686 

OD . LdO 


8 

7.9953473 

8.0721876 

30 

63.75 

60.0 

31 

7 

.670 

9 

61 

2709 

31 

32 

33 

8 

8 

.654 

.637 

71.25 

67.1 

49 

38 

3541 

4375 

32 

33 

10 

78.75 

74.1 

34 

8 

.621 

11 

26 

5209 

34 




86.25 

81.2 




35 

8 

.605 

12 

14 

6044 

35 



93.75 

88.2 

36 

9 

.589 

13 

.9953402 

6879 

36 

37 

38 

9 

.079 

.572 

.556 

101.25 

95.3 

.9953390 

78 

7714 

8550 

37 

38 

14 

108.75 

102.4 

.080 


67 

.0729387 

39 

39 

.540 

15 

116.25 

109.4 

7.9953355 

43 

8.0730224 

1062 

40 

41 

40 

101.080 

84.524 

16 


116.5 

41 

0 

.507 


17 

42 

0 

.491 



31 

1900 

42 

43 

43 

1 

.475 




19 

2739 

44 

1 

.458 




.9953307 

3578 

44 

45 

1 

.442 




.9953295 

4418 

45 

46 

2 

.426 




83 

5259 

46 

47 

2 

.409 




71 

6099 

47 

48 

2 

.393 




60 

6941 

48 

49 

2 

.377 




48 

7783 

49 

50 

101.083 

84.360 




7.9953236 

8.0738625 

50 

51 

3 

.344 




24 

.0739469 

51 

52 

3 

.327 




12 

.0740313 

52 

53 

3 

.311 




.9953200 

1157 

53 

54 

4 

.295 



% 

.9953188 

2002 

54 

55 

4 

.278 




76 

2847 

55 

56 

4 

.262 




64 

3693 

56 

57 

5 

.245 




53 

4539 

57 

58 

5 

.229 




41 

5386 

58 

59 

5 

.213 




29 

6233 

59 

60 

101.085 

84.196 




7.9953117 

1 . 

8.0747081 

60 


25 

























































34 ° 


/ 

M 

P 

/ 

0 

.0098926 

.0118770 

0 

1 

6 

794 

1 

2 

6 

817 

2 

3 

5 

840 

3 

4 

5 

863 

4 

5 

5 

887 

5 

6 

5 

910 

6 

7 

4 

933 

7 

8 

4 

957 

8 

9 

4 

.0118980 

9 

10 

.0098924 

.0119003 

10 

11 

3 

027 

11 

12 

3 

050 

12 

13 

3 

074 

13 

14 

2 

097 

14 

15 

2 

120 

15 

16 

2 

144 

16 

17 

2 

167 

17 

18 

1 

191 

18 

19 

1 

215 

19 

20 

.0098921 

.0119238 

20 

21 

1 

262 

21 

22 

0 

285 

22 

23 

0 

309 

23 

24 

.0098920 

333 

24 

25 

.0098919 

356 

25 

26 

9 

380 

26 

27 

9 

404 

27 

28 

9 

427 

28 

29 

8 

451 

29 

30 

.0098918 

.0119475 

30 

31 

8 

499 

31 

32 

8 

522 

32 

33 

7 

546 

33 

34 

7 

570 

34 

35 

7 

594 

35 

36 

6 

618 

36 

37 

6 

642 

37 

38 

6 

666 

38 

39 

6 

690 

39 

40 

.0098915 

.0119714 

40 

41 

5 

738 

41 

42 

5 

762 

42 

43 

5 

786 

43 

44 

4 

810 

44 

45 

4 

834 

45 

46 

4 

858 

46 

47 

3 

882 

47 

48 

3 

906 

48 

49 

3 

930 

49 

50 

.0098913 

.0119954 

50 

51 

2 

.0119978 

51 

52 

2 

.0120003 

52 

53 

2 

027 

53 

54 

2 

051 

54 

55 

1 

075 

55 

56 

1 

100 

56 

57 

1 

124 

57 

58 

0 

148 

58 

59 

0 

173 

59 

60 

.0098910 

.0120197 

60 


P 

Interpolating Table. 


Tabular Differences. 


diff.P 


23 

24 

25 


tt 

2.6 

ft 

2.5 

// 

2.4 

0 

1 

7.8 

7.5 

7.2 

2 

13.0 

12.5 

12.0 

3 

18.3 

17.5 

16.8 

4 

23.5 

22.5 

21.6 

5 

28.7 

27.5 

26.4 

6 

33.9 

32.5 

31.2 

7 

39.1 

37.5 

36.0 

8 

44.3 

42.5 

40.8 

9 

49.6 

47.5 

45.6 

10 

11 

54.8 

52.5 

50.4 

60.0 

57.5 

55.2 

12 

65.2 

62.5 

60.0 

13 

70.4 

67.5 

64.8 

14 

75.7 

72.5 

69.6 

15 

80.9 

77.5 

74.4 

16 

86.1 

82.5 

79.2 

17 

91.3 

87.5 

84.0 

18 

96.5 

92.5 

88.8 

19 

101.7 

97.5 

93.6 

20 

107.0 

102.5 

98.4 

21 

112.2 

107.5 

103.2 

22 

117.4 

112.5 

108.0 

23 


117.5 

112.8 

24 




117.6 

25 







26 














































































34 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.085 

84.196 

1 

6 

.180 

2 

6 

.163 

3 

6 

.147 

4 

6 

.130 

5 

7 

.114 

6 

7 

.097 

7 

7 

.081 

8 

8 

.064 

9 

8 

.048 

10 

101.088 

84.031 

11 

8 

84.015 

12 

9 

83.998 

13 

9 

.982 

14 

.089 

.965 

15 

.090 

.949 

16 

0 

.932 

17 

0 

.916 

18 

0 

.899 

19 

1 

.882 

20 

101.091 

83.866 

21 

1 

.849 

22 

1 

.833 

23 

2 

.816 

24 

2 

.799 

25 

2 

.783 

26 

3 

.766 

27 

3 

.750 

28 

3 

.733 

29 

3 

.716 

30 

101.094 

83.700 

31 

4 

.683 

32 

4 

.666 

33 

5 

.650 

34 

5 

.633 

35 

5 

.616 

36 

5 

.600 

37 

6 

.583 

38 

6 

.566 

39 

6 

.549 

40 

101.097 

83.533 

41 

7 

.516 

42 

7 

.499 

43 

7 

.482 

44 

8 

.466 

45 

8 

.449 

46 

8 

.432 

47 

8 

.415 

48 

9 

.399 

49 

9 

.382 

50 

101.099 

83.365 

51 

.100 

.348 

52 

0 

.331 

53 

0' 

.315 

54 

0 

.298 

55 

1 

.281 

56 

1 

.264 

57 

1 

.247 

58 

2 

.230 

59 

2 

.214 

60 

101.102 

83.197 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

16 

17 

// 

3.75 

// 

3.5 

0 

1 

11.25 

10.6 

2 

18.75 

17.6 

3 

26.25 

24.7 

4 

33.75 

31.8 

5 

41.25 

38.8 

6 

48.75 

45.9 

7 

56.25 

52.9 

8 

63.75 

60.0 

9 

71.25 

67.1 

10 

78.75 

74.1 

11 

86.25 

81.2 

12 

93.75 

88.2 

13 

101.25 

95.3 

14 

108.75 

102.4 

15 

116.25 

109.4 

16 


116.5 

17 





Log. M 

Log. P 

1 / 

7.9953117 

8.0747081 

0 

.9953105 

7929 

1 

.9953093 

8778 

2 

81 

.0749628 

3 

69 

.0750478 

4 

57 

1328 

5 

45 

2179 

6 

33 

3031 

7 

21 

3883 

8 

.9953009 

4736 

9 

7.9952998 

8.0755589 

10 

86 

6443 

11 

74 

7297 

12 

62 

8152 

13 

50 

9007 

14 

38 

.0759863 

15 

26 

.0760719 

16 

14 

1576 

17 

.9952902 

2434 

18 

.9952890 

3292 

19 

7.9952878 

8.0764150 

20 

66 

5009 

21 

54 

5869 

22 

42 

6729 

23 

30 

7590 

24 

18 

8451 

25 

.9952806 

.0769313 

26 

.9952794 

.0770176 

27 

82 

1038 

28 

70 

1902 

29 

7.9952758 

8.0772766 

30 

46 

3630 

31 

» 34 

4495 

32 

22 

5361 

33 

.9952710 

6227 

34 

.9952698 

7094 

35 

86 

7961 

36 

74 

8829 

37 

62 

.0779697 

38 

50 

.0780566 

39 

7.9952638 

8.0781435 

40 

26 

2305 

41 

14 

3176 

42 

.9952602 

4047 

43 

.9952590 

4918 

44 

78 

5791 

45 

66 

6663 

46 

54 

7536 

47 

42 

8410 

48. 

30 

.0789285 

49 

7.9952518 

8.0790159 

50 

.9952506 

1035 

51 

.9952493 

1911 

52 

81 

2787 

53 

69 

3664 

54 

57 

4542 

55 

45 

5420 

56 

33 

6299 

57 

21 

7178 

58 

.9952409 

8057 

59 

7.9952397 

8.0798938 

60 


27 

































































35 ° 


/ 

M 

P 

/ 

0 

.0098910 

.0120197 

0 

1 

.0098910 

221 

1 

2 

.0098909 

246 

. 2 

3 

9 

270 

3 

4 

9 

295 

4 

5 

9 

319 

5 

6 

8 

344 

6 

7 

8 

368 

7 

8 

8 

393 

8 

9 

7 

417 

9 

10 

.0098907 

.0120442 

10 

11 

7 

466 

11 

12 

7 

491 

12 

13 

6 

516 

13 

14 

6 

540 

14 

15 

6 

565 

15 

16 

5 

590 

16 

17 

5 

614 

17 

18 

5 

639 

18 

19 

5 

664 

19 

20 

.0098904 

.0120688 

20 

21 

4 

713 

21 

22 

4 

738 

22 

23 

4 

763 

23 

24 

3 

788 

24 

25 

3 

813 

25 

26 

3 

838 

26 

27 

2 

862 

27 

28 

2 

887 

28 

29 

2 

912 

29 

30 

.0098902 

.0120937 

30 

31 

1 

962 

31 

32 

1 

.0120987 

32 

33 

1 

.0121012 

33 

34 

1 

037 

34 

35 

0 

062 

35 

36 

0 

087 

36 

37 

.0098900 

113 

37 

38 

.0098899 

138 

38 

39 

9 

163 

39 

40 

.0098899 

.0121188 

40 

41 

9 

213 

41 • 

42 

8 

239 

42 

43 

8 

264 

43 

44 

8 

289 

44 

45 

7 

314 

45 

46 

7 

340 

46 

47 

7 

365 

47 

48 

7 

390 

48 

49 

6 

416 

49 

50 

.0098896 

.0121441 

50 

51 

6 

466 

51 

52 

5 

492 

52 

53 

5 

517 

53 

54 

5 

543 

54 

55 

5 

568 

55 

56 

4 

594 

56 

57 

4 

619 

57 

58 

4 

645 

58 

59 

4 

670 

59 

60 

.0098893 

.0121696 

60 


P 

Interpolating Table. 


Tabular Differences. 


diff.P 


24 

25 

26 


n 

2 5 

// 

2.4 

// 

2.3 

0 

1 

7.5 

7.2 

6.9 

o 

12.5 

12.0 

11.5 

L 

3 

17.5 

16.8 

16.2 

A 

22.5 

21.6 

20.8 


K 

27.5 

26.4 

25.4 

if 

6 

32.5 

31.2 

30.0 

7 




oi .0 

*50. U 

Oi. 0 

8 

42.5 

40.8 

39.2 

9 

47.5 

45.6 

43.8 

10 

52.5 

50.4 

48.5 

11 

57.5 

55.2 

53.1 

12 

62.5 

60.0 

57.7 

13 

67.5 

64.8 

62.3 

14 

72.5 

69.6 

66.9 

15 

77.5 

74.4 

71.5 

16 

82.5 

79.2 

76.2 

17 

87.5 

84.0 

80.8 

18 

92.5 

88.8 

85.4 

19 

97.5 

93.6 

90.0 

20 

102.5 

98.4 

94.6 

21 

107.5 

103.2 

99.2 

22 

112.5 

108.0 

103.8 

23 

117.5 

112.8 

108.5 

24 


117.6 

113.1 


25 



117.7 



26 





28 


















































































35 ° 


f 

Reciprocal 

M 

Reciprocal 

P 





Log. M 

Log. P 

/ 

0 

101.102 

83.197 





7.9952397 

8.0798938 

0 

1 

2 

.180 





85 

.0799819 

1 

2 

3 

.163 





73 

.0800700 

2 

3 

3 

.146 





61 

1582 

3 

4 

3 

.129 





49 

2465 

4 

5 

4 

.112 





36 

3348 

5 

6 

4 

.095 





24 

4231 

6 

7 

4 

.078 





12 

5114 

7 

8 

4 

.062 





.9952300 

5999 

8 

9 

5 

.045 





.9952288 

6884 

9 

10 

101.105 

83.028 





7.9952276 

8.0807770 

10 

11 

5 

83.011 





64 

8656 

11 

12 

5 

82.994 





52 

.0809543 

12 

13 

6 

.977 





40 

.0810431 

13 

14 

6 

.960 





28 

1319 

14 





Reciprocal P 





15 

6 

.943 

Interpolating Table. 


15 

2207 

15 

16 

7 

.926 





.9952203 

3096 

16 






17 

7 

.909 

Tabular Differences. 

diff. 
rep. P 

.9952191 

3986 

17 

18 

7 

.892 




79 

4876 

18 





19 

7 

.875 

16 

17 

18 

67 

5767 

19 

20 

21 

101.108 

8 

82.858 
.841 

n 

3.75 

// 

3.5 

ft 

3.3 

0 

1 

7.9952155 

43 

8.0816658 

7550 

20 

21 

11.25 

10.6 

10.0 

22 

8 

.824 

O 

30 

8443 

22 

23 

24 

9 

.807 

.790 

18.75 

17.6 

16.7 

L 

18 

.9952106 

.0819335 

.0820229 

23 

24 


Q 

9 

26.25 

24.7 

23.3 

6 

A 

25 

9 

.773 

33.75 

31.8 

30.0 

e ± 

.9952094 

1123 

25 

26 

.109 

.756 




* 5 

82 

2018 

26 

41.25 

38.8 

36.7 

O 

27 

.110 

.739 

6 

70 

2913 

27 

28 

0 

.722 

48.75 

45.9 

43.3 

58 

3809 

28 

29 

0 

.705 




7 

45 

4705 

29 

56.25 

52.9 

50.0 

8 

30 

31 

101.111 

1 

82.687 

.670 

63.75 

60.0 

56.7 

7.9952033 

21 

8.0825602 

6499 

30 

31 

9 

71.25 

67.1 

63.3 

32 

1 

.653 

10 

.9952009 

7397 

32 

33 

34 

1 

.636 

.619 

78.75 

74.1 

70.0 

.9951997 

85 

8295 

.0829194 

33 

34 

11 

2 

86.25 

81.2 

76.7 



12 




35 

36 

2 

.602 
„ .585 

93.75 

88.2 

83.3 

73 

60 

.0830093 

0993 

35 

36 

13 

2 

101.25 

95.3 

90.0 

37 

3 

568 

14 

48 

1894 

37 

38 

39 

3 

.551 

.534 

108.75 

102.4 

96.7 

36 

24 

2795 

3697 

38 

39 

15 

16 

3 

116.25 

109.4 

103.3 

40 

101.113 

82.516 


116.5 

110.0 

7.9951912 

.9951899 

8.0834600 

5502 

40 

41 


17 

41 

42 

4 

.499 

482 



116.7 


87 

6406 

42 

4 



18 

43 

4 

.465 




75 

7310 

43 

44 

5 

.448 





63 

8215 

44 

45 

5 

.431 





51 

.0839120 

45 

46 

5 

.413 





38 

.0840026 

46 

47 

5 

.396 





26 

0932 

47 

48 

6 

.379 





14 

1839 

48 

49 

6 

.362 





.9951802 

2746 

49 

50 

101.116 

82.345 





7.9951790 

8.0843653 

50 

51 

7 

.327 





78 

4562 

51 

52 

7 

.310 





65 

5471 

52 

53 

7 

.293 





53 

6380 

53 

54 

7 

.276 





41 

7291 

54 

55 

8 

.258 





29 

8201 

55 

56 

8 

.241 





16 

.0849113 

56 

57 

8 

.224 





.9951704 

.0850025 

57 

58 

9 

.207 





.9951692 

0937 

58 

59 

9 

.189 





80 

1850 

59 

60 

101.119 

82.172 





7.9951668 

8.0852764 

60 


29 



































































36 ° 


M 


0 

.0098893 

1 

3 

2 

3 

3 

2 

4 

2 

5 

2 

6 

2 

7 

1 

8 

1 

9 

1 

10 

.0098890 

11 

0 

12 

0 

13 

.0098890 

14 

.0098889 

15 

9 

16 

9 

17 

9 

18 

8 

19 

8 

20 

.0098888 

21 

7 

22 

7 

23 

•7 

24 

7 

25 

6 

26 

6 

27 

6 

28 

5 

29 

5 

30 

.0098885 

31 

5 

32 

4 

33 

4 

34 

4 

35 

4 

36 

3 

37 

3 

38 

3 

39 

2 

40 

.0098882 

41 

2 

42 

2 

43 

1 

44 

1 

45 

1 

46 

0 

47 

0 

48 

0 

49 

.0098880 

50 

.0098879 

51 

9 

52 

9 

53 

8 

54 

8 

55 

8 

56 

8 

57 

7 

58 

7 

59 

7 

60 

.0098876 


P 

t 

.0121696 

0 

722 

1 

747 

• 2 

773 

3 

799 

4 

824 

5 

850 

6 

876 

7 

902 

8 

927 

9 

.0121953 

10 

.0121979 

11 

.0122005 

12 

031 

13 

057 

14 

083 

15 

108 

16 

134 

17 

160 

. 18 

186 

19 

.0122212 

20 

238 

21 

264 

22 

291 

23 

317 

24 

343 

25 

369 

26 

395 

27 

421 

28 

447 

29 

.0122474 

30 

500 

31 

526 

32 

553 

33 

579 

34 

605 

35 

632 

36 

658 

37 

684 

38 

711 

39 

.0122737 

40 

764 

41 

790 

42 

817 

43 

843 

44 

870 

45 

896 

46 

923 

47 

950 

48 

.0122976 

49 

.0123003 

50 

030 

51 

056 

52 

083 

53 

110 

54 

137 

55 

164 

56 

190 

57 

217 

58 

244 

59 

.0123271 

60 


P 

Interpolating Table. 


Tabular Differences. 

25 

26 

27 

n 

2.4 

// 

2.3 

// 

2.2 

7.2 

6.9 

6.7 

12.0 

11.5 

. 11.1 

16.8 

16.2 

15.6 

21.6 

20.8 

20.0 

26.4 

25.4 

24.4 

31.2 

30 ..0 

28.9 

36.0 

34.6 

33.3 

40.8 

39.2 

37.8 

45.6 

43.8 

42.2 

50.4 

48.5 

46.7 

55.2 

53.1 

51.1 

60.0 

57.7 

55.6 

64.8 

62.3 

60.0 

69.6 

66.9 

64.4 

74.4 

71.5- 

68.9 

79.2 

76.2 

73.3 

84.0 

80.8 

77.8 

88.8 

85.4 

82.2 

93.6 

90.0 

86.7 

98.4 

94.6 

91.1 

103.2 

99.2 

95.6 

108.0 

103.8. 

100.0 

112.8 

108.5 

104.4 

117.6 

113.1 

108.9 


117.7 

113.3 



117.8 







diff. P 


0 

1 

2 

3 

4 

5 

6 
7 


9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 - 

20 
21 
22 

23 

24 

25 

26 
27 


30 


















































































36 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.119 

82.172 

1 

.119 

.155 

2 

.120 

.137 

3 

0 

.120 

4 

0 

.103 

5 

1 

.085 

6 

1 

.068 

7 

1 

.051 

8 

1 

• .033 

9 

2 

82.016 

10 

101.122 

81.999 

11 

2 

.981 

12 

3 

.964 

13 

3 

.947 

14 

3 

.929 

15 

3 

.912 

16 

4 

.894 

17 

4 

.877 

18 

4 

.860 

19 

5 

.842 

20 

101.125 

81.825 

21 

5 

.807 

22 

5 

.790 

23 

6 

.772 

24 

6 

.755 

25 

6 

.738 

26 

7 

.720 

27 

7 

.703 

28 

7 

.685 

29 

7 

.668 

30 

101.128 

81.650 

31 

8 

.633 

32 

8 

.615 

33 

9 

.598 

34 

9 

.580 

35 

-9 

.563 

36 

.129 

- .545 

37 

.130 

.528 

38 

0 

.510 

39 

0 

.492 

40 

101.131 

81.475 

41 

1 

.457 

42 

1 

.440 

43 

1 

.422 

44 

2 

.405 

45 

2 

.387 

46 

2 

.369 

47 

3 

.352 

48 

3 

.334 

49 

3 

.316 

50 

101.133 

81.299 

51 

4 

.281 

52 

4 

.264 

53 

4 

.246 

54 

5 

.228 

55 

5 

.211 

56 

5 

.193 

57 

5 

.175 

58 

6 

.158 

59 

6 

.140 

60 

101.136 

81.122 



Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

17 

18 

ft 

3.5 

// 

3.3 

0 

1 

10.6 

10.0 

2 

17.6 

16.7 

3 

24.7 

23.3 

4 

31.8 

30.0 

5 

38.8 

36.7 

6 

45.9 

43.3 

7 

52.S 

50.0 

8 

60.0 

56.7 

9 

67.1 

63.3 

10 

74.1 

70.0 

11 

81.2 

76.7 

12 

13 

88.2 

83.3 

95.3 

90.0 

14 

102.4 

96.7 

15 

109.4 

T03.3 

16 

116.5 

110.0 

17 


lift 7 


110. ( 

18 





• 

Log. M 

Log. P 

/ 

7.9951668 

8.0852764 

0 

55 

3678 

1 

, 43 

4592 

• 2 

31 

5508 

3 

19 

6422 

4 

.9951606 

7339 

5 

.9951594 

8256 

6 

82 

.0859173 

7 

70 

.0860091 

8 

57 

1010 

9 

7.9951545 

8.0861929 

10 

33 

2849 

11 

21 

3769 

12 

.9951508 

4690 

13 

.9951496 

5612 

14 

84 

6534 

15 

72 

7455 

16 

59 

8378 

17 

47 

.0869302 

18 

35 

.0870226 

19 

7.9951423 

8.0871151 

20 

.9951410 

2077 

21 

.9951398 

3003 

22 

86 

3929 

23 

73 

4856 

24 

61 

5784 

25. 

49 

6711 

26 

37 

7640 

27 

24 

8569 

28 

12 

.0879499 

29 

7.9951300 

8.0880430 

30 

.9951287 

1361 

31 

75 

2293 

32 

63 

3225 

33 

50 

4158 

34 

38 

5091 

35 

26 

6025 

36 

14 

6958 

37 

.9951201 

• 7893 

38 

.9951189 

8829 

39 

7.9951177 

8.0889765 

40 

64 

.0890702 

41 

52 

1639 

42 

40 

2577 

43 

27 

3516 

44 

15 

4455 

45 

.9951103 

5394 

46 

.9951090 

6334 

47 

78 . 

7275 

48 

66 

8216 

49 

7.9951053 

8.0899158 

50 

41 

.0900100 

51 

29 

1043 

52 

16 

1987 

53 

.9951004 

2931 

54 

.9950992 

3875 

55 

79 

4821 

56 

67 

5767 

57 

55 

6713 

58 

' 42 

7660 

59 

7.9950930 

8.0908608 

60 


31 







































































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


37 ° 


M 

P 

t 





0098876 

6 

6 

6 

5 

.0123271 

298 

325 

352 

379 

0 

1 

2 

3 

4 





5 

5 

5 

4 

4 

406 

433 

460 

487 

514 

5 

6 

7 

8 

9 

P 

Interpolating Table. 


0098874 

.0123541 

10 

Tabular Differences. 

diff. P 

3 

3 

568 
595 
. 623 

11 

12 

13 

27 

28 

29 

3 

// 

2.2 

// 

2.1 

// 

2.1 

0 

3 

650 

14 

1 




6.7 

6.4 

6.2 


677 

15 

9 

2 

11.1 

10.7 

10.3 

4 

2 

704 

16 

3 

9 

732 

759 

17 

18 

15.6 

15.0 

14.5 


4 

1 

20.0 

19.3 

18.6 

1 

786 

19 

K 




24.4 

23.6 

22.8 

0 

.0098871 

.0123814 

20 

6 

28.9 

27.9 

26.9 

1 

841 

21 

7 

0 

0 

868 

896 

22 

23 

33.3 

32.1 

31.0 

8 

37.8 

36.4 

35.2 

.0098870 

923 

24 

9 




A 0 o 

40 7 

qq 3 

.0098869 

951 

25 

rt4 . 4 


oy. o 

10 

46.7 

45.0 

43.4 

9 

.0123978 

26 

11 

9 

9 

.0124006 

033 

27 
' 28 

51.1 

49.3 

47.6 

12 

55.6 

53.6 

51.7 

8 

061 

29 

13 




60.0 

57.9 

55.9 

.0098868 

.0124088 

30 

14 

64.4 

62.1 

60.0 

8 

116 

31 

15 

7 

143 

171 

32 

33 

68.9 

66.4 

64.1 

7 

16 

73.3 

70.7 

68.3 

7 

199 

34 

17 




•77.8 

75.0 

72.4 

7 

226 

35 

18 

82.2 

79.3 

76.6 

6 

254 

36 

19 

6 

282 

310 

37 

38 

86.7 

83.6 

80.7 

6 

20 

91.1 

87.9 

84.8 

5 

337 

39 

21 




95.6 

92.1 

89.0 

.0098865 

.0124365 

40 

99 

100.0 

96.4 

93.1 

44 

5 

3 3 

41 

23 

5 

421 

449 

42 

43 

104.4 

100.7 

97.2 

4 

9/1 

108.9 

105.0 

101.4 


4 

477 

44 

9K 




113.3 

109.3 

105.5 

40 

4 

504 

532 

45 

26 

117.8 

113.6 

109.7 

3 

46 

27 

3 

560 

588 

616 

47 

48 

49 


117.9 

113.8 

3 

3 


9Q 



117.9 

40 



29 

.0098862 

2 

2 

2 

1 

.0124644 

672 

700 

729 

757 

50 

51 

52 

53 

54 








1 

1 

0 

0 

0 

.0098860 

785 

813 

841 

869 

898 

.0124926 

55 

56 

57 

58 

59 

60 






32 












































































37 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.136 

81.122 

1 

7 

.104 

2 

7 

.087 

3 

7 

.069 

4 

7 

.051 

5 

8 

.034 

6 

8 

81.016 

7 

8 

80.998 

8 

9 

.980 

9 

9 

.962 

10 

101.139 

80.945 

11 

.139 

.927 

12 

.140 

.909 

13 

0 

.891 

14 

0 

.874 

15 

1 

.856 

16 

1 

.838 

17 

1 

.820 

18 

1 

.802 

19 

2 

.784 

20 

101.142 

80.767 

21 

2 

.749 

22 

3 

.731 

23 

3 

.713 

24 

3 

.695 

25 

4 

.677 

26 

4 

.659 

27 

4 

.642 

28 

4 

.624 

29 

5 

.606 

30 

101.145 

80.588 

31 

5 

.570 

32 

6 

.552 

33 

6 

.534 

34 

6 

.516 

35 

6 

.498 

36 

7 

.480 

37 

7 

.462 

38 

7 

.444 

39 

8 

.426 

40 

101.148 

80.408 

41 

8 

.390 

42 

8 

.372 

43 

9 

.354 

44 

9 

.336 

45 

.149 

.318 

46 

.150 

.300 

47 

0 

.282 

48 

0 

.264 

49 

0 

.246 

50 

101.151 

80.228 

51 

1 

.210 

52 

1 

.192 

53 

2 

.174 

54 

2 

.156 

55 

2 

.138 

56 

2 

.120 

57 

3 

.102 

58 

3 

.084 

59 

3 

.066 

60 

101.154 

80.047 


Reciprocal P 
InterpolatingTable. 


Tabular Differences. 


17 

18 

19 

// 

// 

tt 

3.5 

3.3 

3.2 

10.6 

10.0 

9.5 

17.6 

16.7 

15.8 

24.7 

23.3 

22.1 

31.8 

30.0 

28.4 

38.8 

36.7 

34.7 

45.9 

43.3 

41.1 

52.9 

50.0 

47,4 

60.0 

56.7 

53.7 

67.1 

63.3 

60.0 

74.1 

70.0 

66.3 

81.2 

76.7 

72.6 

88.2 

83.3 

78.9 

95.3 

90.0 

85.3 

102.4 

96.7 

91.6 

109.4 

103.3 

97.9 

116.5 

110.0 

104.2 


116.7 

110.5 




116.8 








Log. M 

Log. P 

/ 


7.9950930 

8.0908608 

0 


18 

.0909556 

1 


.9950905 

.0910505 

2 


.9950893 

1453 

3 


80 

2403 

4 


68 

3354 

5 


56 

4305 

6 

1 

43 

5257 

7 


31 

6209 

8 


19 

7162 

9 


7.9950806 

8.0918115 

10 


.9950794 

.0919068 

11 


81 

.0920023 

12 


69 

0978 

13 


57 

1934 

14 


44 

2890 

15 


32 

3847 

16 

difif. 

19 

4805 

17 

rep. P , 

.9950707 

5763 

18 

0 

.9950695 

6721 

19 

1 

7.9950682 

8.0927680 

20 

2 

70 

8640 

21 

Q 

58 

.0929600 

22 

o 

45 

.0930561 

23 

4 

33 

1523 

24 

5 

20 

2485 

25 

6 

.9950608 

3447 

26 


.9950595 

4410 

27 

7 

83 

5374 

28 

8 

71 

6338 

29 

9 

7.9950558 

8.0937303 

30 

10 

46 

8269 

31 

■1 1 

33 

.0939235 

32 

11 

21 

.0940202 

33 

12 

.9950509 

1169 

34 

13 

.9950496 

2137 

35 

14 

84 

3105 

36 


71 

4074 

37 

15 

59 

5044 

38 

16 

46 

6014 

39 

17 

7.9950434 

8.0946985 

40 

18 

22 

7956 

41 


.9950409 

8928 

42 

19 

.9950397 

.0949901 

43 


84 

.0950874 

44 


72 

1848 

45 


59 

2822 

46 


47 

3796 

47 


34 

4772 

48 


22 

5748 

49 


7.9950309 

8.0956725 

50 


.9950297 

7702 

51 


84 

8680 

52 


72 

.0959658 

53 


60 

.0960637 

54 


47 

1617 

55 


35 

2597 

56 


22 

3578 

57 


.9950210 

4560 

58 


.9950197 

5542 

59 


7.9950185 

8.0966524 

60 


33 










































































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 


38 ° 


M 

P 

/ 

.0098860 

.0124926 

0 

.0098859 

954 

1 

9 

.0124982 

2 

9 

.0125011 

3 

8 

039 

4 

8 

068 

5 

8 

096 

6 

8 

124 

7 

7 

153 

8 

7 

181 

9 

.0098857 

.0125210 

10 

6 

238 

11 

6 

267 

12 

6 

' 295 

13 

6 

324 

14* 

5 

353 

15 ! 

5 

381 

16 

5 

410 

17 

4 

439 

18 

4 

467 

19 

.0098854 

.0125496 

20 

4 

525 

21 

3 

554 

22 

3 

582 

23 

3 

611 

24 

2 

640 

25 

2 

669 

26 

2 

698 

27 

2 

727 

28 

1 

756 

29 

.0098851 

.0125785 

30 

1 

814 

31 

0 

843 

32 

0 

872 

33 

0 

901 

34 

.0098850 

930 

35 

.0098849 

959 

36 

9 

.0125988 

37 

9 

.0126017 

38 

8 

047 

39 

.0098848 

.0126076 

40 

8 

105 

41 

8 

134 

42 

7 

163 

43 

7 

193 

44 

7 

222 

45 

6 

251 

46 

6 

281 

47 

6 

310 

48 

6 

340 

49 

.0098845 

.0126369 

50 

5 

399 

51 

5 

428 

52 

4 

458 

53 

4 

487 

54 

4 

517 

55 

4 

546 

56 

3 

576 

57 

3 

606 

58 

3 

635 

59 

.0098842 

.0126665 

60 


Interpolating Table. 


Tabular Differences. 


28 


2.1 


6.4 


10.7 


15.0 


19.3 


23.6 


27.9 


32.1 


36.4 

40.7 


45.0 


49.3 


53.6 


57.9 


62.1 


66.4 


70.7 


75.0 


79.3 


83.6 

87.9 

92.1 


96.4 


100.7 


105.0 


109.3 


113.6 


117.9 


29 


2.1 


6.2 


10.3 


14.5 


18.6 


22.8 


26.9 


31.0 


35.2 


39.3 


43.4 


47.6 


51.7 


55.9 


60.0 


64.1 


68.3 


72.4 


76.6 


80.7 


84.8 


89.0 


93.1 


97.2 


101.4 


105.5 


109.7 


113.8 


117.9 


30 


2.0 


6.0 


10.0 


14.0 


18.0 


22.0 


26.0 


30.0 


34.0 


38.0 


42.0 


46.0 


50.0 


54.0 


58.0 


62.0 


66.0 


70.0 


74.0 


78.0 


82.0 


86.0 


90.0 


94.0 


98.0 


102.0 


106.0 


110.0 


114.0 


118.0 


diff. P 


l 

2 

3 

4 

- 5 

6 

7 

- 8 

9 

- 10 

11 

- 12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

■ 22 

23 

- 24 

- 25 

26 

27 

- 28 

- 29 


34 






























































































38 ° 


/ 

Reciprocal 

Reciprocal 




Log. M 

Log. P 

/ 


M 

P 





0 

101.154 

80.047 




7.9950185 

8.0966524 

0 

1 

4 

.029 




72 

7507 

1 

2 

4 

80.011 




60 

8491 

2 

3 

5 

79.993 




47 

.0969475 

3 

4 

5 

.975 




35 

.0970460 

4 

5 

5 

.957 




22 

1446 

5 

6 

5 

.939 




.9950110 

2431 

6 

7 

6 

.921 




.9950097 

3418 

7 

8 

6 

.902 




85 

4406 

8 

9 

6 

.884 




72 

5394 

9 

10 

101.157 

79.866 




1 7.9950060 

8.0976382 

10 

11 

7 

.848 




47 

7371 

11 

12 

7 

.830 




35 

8360 

12 

13 

7 

.811 




22 

.0979351 

13 

14 

8 

.793 

Reciprocal P 

Interpolating Table. 

.9950010 

.0980342 

14 

15 

8 

.775 




.9949997 

85 

1333 

2326 

15 

16 

16 

8 

.757 

Tahtilar Diff. 

diff. 
rep. P 

17 

9 

.739 



72 

3318 

17 




18 

9 

.720 

18 

19 

60 

4311 

18 

19 

9 

.702 

// 

/ / 

0 

47 

5305 

19 

20 

101.159 

79.684 

3.3 

3.2 

7.9949935 

8.0986299 

20 

1 

10.0 

9.5 

21 

.160 

.666 

2 

22 

7295 

21 

22 

23 

0 

0 

.647 

.629 

16.7 

15.8 

.9949910 

.9949897 

8290 

.0989287 

22 

23 

. 3 

23.3 

22.1 

24 

1 

.611 

4. 

85 

.0990283 

24 

25 

1 

.592 

30.0 

28.4 

‘I 

5 

72 

1280 

25 

36.7 

34.7 

- 26 

1 

.574 

A 

59 

2279 

26 

27 

28 

2 

2 

.556 

.538 

43.3 

41.1 

0 

7 

47 

35 

3277 

4277 

27 

28 

50.0 

47.4 

29 

2 

.519 

8 

22 

5276 

29 

30 

101.162 

79.501 

56.7 

53.7 

7.9949810 

8.0996276 

30 

9 

63.3 

60.0 

31 

3 

.483 

10 

.9949797 

7277 

31 

32 

33 

3 

3 

.464 

.446 

70.0 

66.3 

85 

72 

8279 

.0999282 

32 

33 

11 

76.7 

72.6 

34 

4 

.428 

12 

59 

. 1000285 

34 

35 

4 

.409 

83.3 

78.9 

47 

1287 

35 

13 

90.0 

85.3 

36 

4 

.391 

14 

34 

2291 

36 

37 

38 

4 

5 

.373 

.354 

96.7 

91.6 

22 

.9949709 

3296 

4302 

37 

38 

15 

103.3 

97.9 

39 

5 

.336 

16 

17 

.9949697 

5308 

39 

40 

101.165 

79.317 

110.0 

104.2 

7.9949684 

8.1006314 

40 


110.5 

41 

6 

.299 

116.7 

18 

72 

7320 

41 

42 

6 

.281 


116.8 

59 

8328 

42 

43 ' 

6 

.262 


19 

46 

.1009337 

43 



44 

45 

6 

.244 




34 

.1010346 

44 

7 

.225 




21 

1355 

45 

46 

7 

.207. 




.9949609 

2364 

46 

47 

7 

.189 




.9949596 

3375 

47 

48 

8 

.170 




84 

4387 

48 

49 

8 

.152 




71 

5399 

49 

50 

101.168 

79.133 




7.9949559 

8.1016411 

50 

51 

9 

.115 




46 

7425 

51 

52 

9 

.096 




34 

8437 

52 

53 

9 

.078 




21 

.1019452 

53 

54 

.169 

.059 




.9949508 

.1020467 

54 

55 

.170 

.041 




.9949496 

1483 

55 

56 

0 

.022 




83 

2498 

56 

57 

0 

79.004 




71 

3515 

57 

58 

1 

78.985 




58 

4532 

58 

59 

1 

.967 




45 

5550 

59 

60 

101.171 

78.948 




7.9949433 

8.1026569 

60 


35 









































































/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


39 ° 


M 

P 

/ 

.0098842 

.0126665 

0 

2 

695 

1 

2 

725 

2 

2 

754 

3 

1 

784 

4 

1* 

814 

5 

1 

844 

6 

0 

874 

7 

0 

904 

8 

0 

934 

9 

.0098840 

.0126963 

10 

.0098839 

.0126993 

11 

9 

.0127023 

12 

9 

053 

13 

8 

084 

14 

8 

114 

15 

8 

144 

16 

8 

174 

17 

7 

204 

18 

7 

234 

19 

.0098837 

.0127264 

20 

6 

295 

21 

6 

325 

22 

6 

355 

23 

6 

385 

24 

5 

416 

25 

5 

446 

26 

5 

476 

27 

4 

507 

28 

4 

537 

29 

.0098834 

.0127568 

30 

4 

598 

31 

3 

629 

32 

3 

659 

33 

3 

690 

34 

*2 

720 

35 

2 

751 

36 

2 

782 

37 

2 

812 

38 

1 

843 

39 

.0098831 

.0127874 

40 

1 

904 

41 

0 

935 

42 

0 

966 

43 

.0098830 

.0127997 

44 

.0098829 

.0128028 

45 

9 

058 

46 

9 

089 

47 

9 

120 

v 48 

8 

151 

49 

.0098828 

.0128182 

50 

' 8 

213 

51 

7 

244 

52 

7 

275 

53 

7 

306 

54 

7 

337 

55 

6 

368 

56 

6 

400 

57 

6 

431 

58 

5 

462 

59 

.0098825 

.0128493 

60 


P 

Interpolating Table. 


Tabular Differences. 

diff.P 

29 

30 

31 

32 

n 

2.1 

n 

2.0 

II 

1.9 

II 

1.9 

0 

l 

6.2 

6.0 

5.8 

5.6 

2 

10.3 

10.0 

9.7 

9.4 

3 

14.5 

14.0 

13.5 

13.1 

4 

18.6 

18.0 

17.4 

16.9 

5 

22.8 

22.0 

21.3 

20.6 

6 

26.9 

26.0 

25.2 

24.4 

7 

31.0 

30.0 

29.0 

28.1 

8 

35.2 

34.0 

32.9 

31.9 

9 

39.3 

38.0 

36.8 

35.6 

10 

43.4 

42.0 

40.6 

39.4 

11 

47.6 

46.0 

44.5 

43.1 

12 

51.7 

50.0 

48.4 

46.9 

13 

55.9 

54.0 

52.3 

50.6 

14 

60.0 

58.0 

56.1 

54.4 

15 

64.1 

62.0 

60.0 

58.1 

16 

68.3 

66.0 

63.9 

61.9 

17 

72.4 

70.0 

67.7 

65.6 

18 

76.6 

74.0 

71.6 

69.4 

19 

80.7 | 78.0 

75.5 

73.1 

20 

84.8 

82.0 

79.4 

76.9 

21 

89.0 ! 86.0 

83.2 

80.6 

22 

93.1 

90.0 

87.1 

84.4 

23 

97.2 

94.0 

91.0 

88.1 

24 

101.4 

98.0 

94.8 

91.9 

25 

105.5 

102.0 

98.7 

95.6 

26 

109.7 

106.0 

102.6 

99.4 

27 

113.8 

110.0 

106.5 

103.1 

28 

117.9 

114.0 

• 

110.3 

106.9 

29 


118.0 

114.2 

110.6 

30 




118.1 

114.4 

31 




.j 


118.1 

32 





1 




36 









































































































39 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.171 

78.948 

1 

1 

.930 

2 

2 

.911 

3 

2 

.893 

4 

2 

.874 

5 

3 

.856 

6 

3 

.837 

7 

3 

.819 

8 

4 

.800 

9 

4 

.781 

10 

101.174 

78.763 

11 

4 

.744 

12 

5 

.726 

13 

5 

.707 

14 

5 

.688 

15 

6 

.670 

16 

6 

.651 

17 

6 

.633 

18 

6 

.614 

19 

7 

.595 

20 

101.177 

78.577 

21 

7 

.558 

22 

8 

.539 

23 

8 

.521 

24 

8 

.502 

25 

8 

.483 

26 

9 

.465 

27 

9 

.446 

28 

.179 

.427 

29 

.180 

.408 

30 

101.180 

78.390 

31 

0 

.371 

32 

1 

.352 

33 

1 

.334 

34 

1 

.315 

35 

1 

.296 

36 

2 

.277 

37 

2 

.259 

38 

2 

.240 

39 

3 

.221 

40 

101.183 

78.202 

41 

3 

.183 

42 

3 

.165 

43 

4 

.146 

44 

4 

.127 

45 

4 

.108 

46 

5 

.089 

47 

5 

.071 

48 

5 

.052 

49 

6 

.033 

50 

101.186 

78.014 

51 

6 

77.995 

52 

6 

.976 

53 

7 

.957 

54 

7 

.939 

55 

7 

.920 

56 

8 

.901 

57 

8 

.882 

• 58 

8 

.863 

59 

9 

.844 

60 

101.189 

77.825 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

18 

19 

It 

3.3 

It 

3.2 

0 

1 

10.0 

9.5 

2 

16.7 

15.8 

3 

23.3 

22.1 

4 

30.0 

28.4 

5 

36.7 

34.7 

6 

43.3 

41.1 

7 

50.0 

47.4 

8 

56.7 

53.7 

9 

63.3 

60.0 

10 

70.0 

66.3 

11 

76.7 

72.6 

12 

83.3 

78.9 

13 

90.0 

85.3 

14 

96.7 

91.6 

15 

103.3 

97.9 

16 

1 1 A A 

mi o 

11U . U 


17 

116.7 

110.5 

18 


116.8 

19 





Log. M 

Log. P 

/ 

7.9949433 

8.1026569 

0 

20 

7588 

1 

.9949408 

8607 

2 

.9949395 

.1029628 

2 

83 

.1030649 

4 

70 

1671 

5 

57 

2693 

6 

45 

3715 

7 

32 

4739 

8 

20 

5763 

9 

7.9949307 

8.1036788 

10> 

.9949294 

7813 

11 

82 

8838 

12 

69 

.1039865 

13 

56 

.1040892 

14 

44 

1920 

15 

31 

2948 

16 

19 

3976 

17 

.9949206 

5006 

18. 

.9949194 

6036 

19 

7.9949181 

8.1047067 

20 1 

68 

8099 

21 

56 

.1049130 

22 

43 

.1050163 

23 

31 

1196 

24 

18 

2230 

25 

.9949105 

3265 

26 

.9949093 

4299 

27 

80 

5335 

28 

67 

6371 

29 

7.9949055 

8.1057408 

39 

42 

8446 

31 

30 

.1059483 

32 

17 

.1060522 

33 

.9949004 

1562 

34 

.9948992 

2602 

35 

79 

3643 

36 

66 

4683 

37 

54 

5725 

38. 

41 

6768 

39 

7.9948929 

8.1067811 

40 

16 

8854 

41 

.9948903 

.1069899 

42 

.9948891 

.1070944 

43 

78 

1990 

44 

65 

3036 

45 

53 

4082 

46 

40 

5130 

47 

27 

6178 

48. 

15 

7227 

49 

7.9948802 

8.1078276 

50- 

.9948789 

.1079325 

5L 

77 

.1080376 

52 

64 

1427 

53 

51 

2479 

54 

39 

3532 

55 

26 

4584- 

56 

13 

5638 

57' 

.9948701 

6692 

58'. 

.9948688 

7748 

59 

7.9948675 

8.1088802 

60 


37 










































































40 ° 


/ 

M 

P 

/ 

0 

.0098825 

.0128493 

0 

1 

5 

524 

1 

2 

5 

556 

2 1 

3 

4 

587 

3 

4 

4 

618 

4 

5 

4 

650 

5 

6 

3 

681 

6 

7 

3 

713 

7 

8 

3 

744 

8 

9 

3 

775 

9 

10 

.0098822 

.0128807 

10 

11 

2 

838 

11 

12 

2 

870 

12 

13 

1 

902 

13 

14 

1 

933 

14 

15 

1 

965 

15 

16 

1 

.0128996 

16 

17 

0 

.0129028 

17 

18 

0 

060 

18 

19 

.0098820 

092 

19 

20 

.0098819 

.0129123 

20 

21 

9 

155 

21 

22 

9 

187 

22 

23 

9 

219 

23 

24 

8 

251 

24 

25 

8 

282 

25 

26 

8 

314 

26 

:27 

7 

346 

27 

28 

7 

378 

28 

29 

7 

410 

29 

•‘30 

.0098817 

.0129442 

30 

31 

6 

474 

31 

32 

6 

506 

32 

:33 

6 

538 

33 

34 

5 

571 

34 

35 

5 

603 

35 

36 

5 

635 

36 

37 

4 

667 

37 

38 

4 

699 

38 

39 

4 

732 

39 

40 

.0098814 

.0129764 

40 

41 

3 

796 

41 

42 

3 

829 

42 

43 

3 

861 

43 

44 

2 

893 

44 

45 

2 

926 

45 

46 

2 

958 

46 

47 

2 

.01-29991 

47 

48 

1 

.0130023 

48 

49 

1 

056 

49 

,50 

.0098811 

.0130088 

50 

51 

0 

121 

51 

.52 

0 

154 

52 

53 

0 

186 

53 

.54 

.0098810 

219 

54 

,55 

.0098809 

252 

55 

.56 

9 

284 

56 

57 

9 

317 

57 

58 

8 

350 

58 

59 

8 

383 

59 

60 

.0098808 

.0130415 

60 


P 

Interpolating Table. 


Tabular Differences. 


diff.P 


31 

32 

33 


n 

1.9 

// 

1.9 

ff 

1.8 

0 

1 

5.8 

5.6 

5.5 

2 

9.7 

9.4 

9.1 

3 

13.5 

13.1 

12.7 

4 

17.4 

16.9 

16.4 

5 

21.3 

20.6 

20.0 

6 

25.2 

24.4 

23.6 

7 

29.0 

28.1 

27.3 

8 

32.9 

31.9 

30.9 

9 

36.8 

35.6 

34.5 

10 

40.6 

39.4 

38.2 

11 

44.5 

43.1 

41.8 

12 

48.4 

46.9 

45.5 

13 

52.3 

50.6 

49.1 

14 

56.1 

54.4 

52.7 

15 

60.0 

58.1 

56.4 

16 

63.9 

61.9 

60.0 

17 

67.7 

65.6 

63.6 

18 

71.6 

69.4 

67.3 

19 

75.5 

73.1 

70.9 

20 

79.4 

76.9 

74.5 

21 

83 . 2 , 

80.6 

78.2 

22 

87.1 

84.4 

81.8 

23 

91.0 

88.1 

85.5 

24 

94.8 

91.9 

89.1 

25 

98.7 

95.6 

92.7 

26 

102.6 

99.4 

96.4 

27 

106.5 

103.1 

100.0 

28 

110.3 

106.9 

103.6 

29 

114.2 

110.6 

107.3 

30 

118.1 

114.4 

110.9 

31 


118.1 

114.5 

32 




118.2 

33 







38 

































































































40 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.189 

77.825 

1 

9 

.806 

2 

.189 

.787 

3 

.190 

.768 

4 

0 

.749 

5 

0 

.730 

6 

1 

.711 

7 

1 

.693 

8 

1 

.674 

9 

1 

.655 

10 

101.192 

77.636 

11 

2 

.617 

12 

2 

.598 

13 

3 

.579 

14 

3 

.560 

15 

3 

.541 

16 

4 

.522 

17 

4 

.503 

18 

4 

.483 

19 

4 

.464 

20 

101.195 

77.445 

21 

5 

.426 

22 

5 

.407 

23 

6 

.388 

24 

6 

.369 

25 

6 

.350 

26 

6 

.331 

27 

7 

.312 

28 

7 

.293 

29 

7 

.274 

30 

101.198 

77.255 

31 

8 

.235 

32 

8 

.216 

33 

9 

.197 

34 

9 

.178 

35 

9 

.159 

36 

.199 

.140 

37 

.200 

.121 

38 

0 

.101 

39 

0 

.082 

40 

101.201 

77.063 

41 

1 

.044 

42 

1 

.025 

43 

2 

77.005 

44 

2 

76.986 

45 

2 

.967 

46 

2 

.948 

47 

3 

.929 . 

48 

3 

.909 

49 

3 

.890 

50 

101.204 

76.871 

51 

4 

.852 

52 

4 

.832 

53 

4 

.813 

54 

5 

.794 

55 

5 

.775 

56 

5 

.755 

57 

6 

.736 

58 

6 

.717 

59 

6 

.697 

60 

101.207 

76.678 


Reciprocal P 
Interpolating Table. 


Tabular Differences. 


18 

19 

20 

ft 

3.3 

// 

3.2 

n 

3.0 

10.0 

9.5 

9.0 

16.7 

15.8 

15.0 

23.3 

22.1 

21.0 

30.0 

28.4 

27.0 

36.7 

34.7 

33.0 

43.3 

41.1 

39.0 

50.0 

47.4 

45.0 

56.7 

53.7 

51.0 

63.3 

60.0 

57.0 

70.0 

66.3 

63.0 

76.7 

72.6 

69.0 

83.3 

78.9 

75.0 

90.0 

85.3 

81.0 

96.7 

91.6 

87.0 

103.3 

97.9 

93.0 

110.0 

104.2 

99.0 

116.7 

110.5 

105.0 


116.8 

111.0 



117 0 








. 

Log. M 

Log. P 

r 


7.9948675 

8.1088802 

0 


63 

.1089859 

I 


50 

.1090916 

2 


37 

1973 

8 


25 

3031 

4 


.9948612 

4089 

5 


.9948599 

5149 

6 


87 

6209 

7 


74 

7269 

8 


61 

8330 

9 


7.9948549 

8.1099392 

10 


36 

.1100455 

11 


23 

1518 

12 


.9948511 

2581 

13 


.9948498 

3645 

14 


85 

4711 

15 

diff. 

73 

5776 

16 

rep. P 

60 

6842 

17 


47 

7909 

18 

0 

35 

.1108977 

19 

1 

7.9948422 

8.1110045 

20 

2 

.9948409 

1114 

21 

3 

.9948396 

2182 

22: 


84 

3253 

23 

4 

71 

4323 

24 

5 

58 

5395 

25 

6 

46 

6466 

26 

7 

33 

7539 

27: 

i 

20 

8612 

28 

8 

.9948308 

.1119686 

29 

9 

7.9948295 

8.1120760 

30' 

10 

82 

1835 

31 

1 1 

69 

2911 

32 

11 

57 

' 3988 

33 

12 

44 

5065 

34 

13 

31 

6142 

35. 

14 

19 

7220 

36 


.9948206 

8299 

37 


.9948193 

.1129379 

38 

16 

81 

.1130458 

39 

17 

7.9948168 

8.1131539 

40 

18 

55 ! 

2621 

41 

IQ 

42 

3703 

42: 


30 

4785 

43 

20 

17 

5869 

44 


.9948104 

6953 

45 


.9948091 

8038 

46 


79 

.1139122 

47 


66 

.1140209 

48 


53 

1295 

49 


7.9948041 

8.1142383 

50 


28 

3470 

51 


15 

4559 

52: 


.9948002 

5648 

53 


.9947990 

6738 

54 


77 

7829 

55 


64 

.1148919 

56 


51 

.1150011 

5 r 


39 

1103 

58 


26 

2196 

59 


7.9947913 

8.1153289 

60 


39 


















































































41 ° 


t 

M 

P 

' j 
• 

0 

.0098808 

.0130415 

0 | 

1 

8 

448 

1 

2 

7 

481 

2 ! 

3 

7 

514 

3 

4 

7 

547 

4 

5 

6 

580 

5 

6 

6 

613 

6 

7 

6 

646 

7 

8 

6 

679 

8 

9 

5 

712 

9 

10 

.0098805 

.0130745 

10 

11 

5 

778 

11 

12 

4 

812 

12 

13 

4 

845 

13 

14 

4 

878 

14 

15 

3 

911 

15 

16 

3 

945 

16 

17 

3 

.0130978 

17 

18 

3 

.0131011 

18 

19 

2 

045 

19 

20 

.0098802 

.0131078 

20 

21 

2 

111 

21 

22 

1 

145 

22 

23 

1 

178 

23 

24 

1 

212 

24 

25 

1 

245 

25 

26 

0 

279 

26 

27 

0 

313 

27 

28 

.0098800 

346 

28 

29 

.0098799 

380 

29 

30 

.0098799 

.0131414 

30 I 

31 

9 

447 

31 

32 

9 

481 

32 

33 

8 

515 

33 

34 

8 

548 

34 

35 

8 

582 

35 | 

36 

7 

616 

36 1 

37 

7 

650 

37 

38 

7 

684 

38 J 

39 

7 

718 

39 ! 

i 

40 

.0098796 

.0131752 

40 ! 

41 

6 

786 

41 

42 

6 

820 

42 

43 

5 

854 

43 

44 

5 

888 

44 

45 

5 

922 

45 

46 

4 

956 

46 

47 

4 

.0131990 

47 

48 

4 

.0132025 

48 

49 

4 

059 

49 

50 

.0098793 

.0132093 

50 

51 

3 

127 

51 

52 

3 

162 

52 

53 

2 

196 

53 

54 

2 

230 

54 

55 

2 

265 

55 

.56 

2 

299 

56 

57 

1 

334 

57 

58 

1 

368 

58 

59 

1 

403 

59 

60 

.0098790 

.0132437 

60 


P 

Interpolating Table. 


Tabular Differences. 


33 

34 

35 


// 

1.8 

t // 

1.8 

// 

1.7 

0 

1 

5.5 

5.3 

5.1 

0 

9.1 

I 8.8 

8.6 

ii 


12.7 

12.4 

12.0 

u 

4 

16.4 

15.9 

15.4 


* 

20.0 

: 19.4 

18.9 

o 

6 

23.6 

22.9 

22.3 

7 

27.3 

26.5 

25.7 


8 

30.9 

30.0 

29.1 

0 

34.5 

33.5 

32.6 

i/ 

10 

38.2 

37.1 

36.0 

11 

41.8 

40.6 

39.4 

12 

45.5 

44.1 

42.9 

13 

49.1 

47.6 

46.3 

14 

52.7 

51.2 

49.7 

15 

56.4 

54.7 

53.1 

16 

60.0 

58.2 

56.6 

17 

63.6 

61.8 

60.0 

18 

A7 Q 


AQ A 

0/ . 6 

DO . 6 

Do. 4 

19 

70.9 

63.8 

66.9 

20 

74.5 

72.4 

70.3 

21 

78.2 

75.9 

73.7 

22 

81.8 

79.4 

77.1 

23 

85.5 

82.9 

80.6 

24 

89.1 

86.5 

84.0 

25 

92.7 

90.0 

87.4 

26 

96.4 

93.5 

90.9 

27 

100.0 

97.1 

94.3 

28 

103.6 

100.6 

97.7 

29" 

107.3 

104.1 

101.1 

30 

110.9 

107.6 

104.6 

31 

114.5 

111.2 

108.0 

32 

118.2 

114.7 

111.4 

33 


118.2 

114.9 




34 



118.3 




35 





40 








































































































41 ° 



Reciprocal 

M 

Reciprocal 

P 

0 

101.207 

76.678 

1 

7 

.659 

2 

7 

.639 

3 

7 

.620 

4 

8 

.601 

5 

8 

.581 

6 

8 

.562 

7 

9 

.543 

8 

9 

.523 

9 

.209 

.504 

10 

101.210 

76.485 

11 

0 

.465 

12 

0 

.446 

13 

0 

.426 

14 

1 

.407 

15 

1 

.388 , 

16 

1 

.368 

17 

2 

.349 

18 

2 

.329 

19 

2 

.310 

20 

101.213 

76.290 

21 

3 

.271 

22 

3 

.252 

23 

3 

.232 

24 

4 

.213 

25 

4 

.193 

26 

4 

.174 

27 

5 

.154 

28 

5 

.135 

29 

5 

.115 

30 

101.215 

76.096 

31 

6 

.076 

32 

6 

.057 

33 

6 

.037 

34 

7 

76.018 

35 

i 

75.998 

36 

7 

.979 

37 

8 

.959 

38 

8 

.939 

39 

8 

.920 

40 

101.218 

75.900 

41 

9 

.881 

42 

9 

.861 

43 

.219 

.842 

44 

.220 

.822 

45 

0 

.802 

46 

0 

.783 

47 

1 

.763 

48 

1 

.743 

49 

1 

.724 

50 

101.221 

75.704 

51 

2 

.685 

52 

2 

.665 

53 

2 ‘ 

.645 

54 

3 

.626 

55 

3 

.606 

56 

3 

.586 

57 

4 

.567 

58 

4 

.547 

59 

4 

.527 

60 

101.224 

75.508 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

19 

20 

n 

3,2 

tt 

3.0 

0 

1 

9.5 

9.0 

2 

15.8 

15.0 

3 

22.1 

21.0 

4 

28.4 

27.0 

5 

34.7 

33.0 

6 

41.1 

39.0 

7 

47.4 

45.0 

8 

53.7 

51.0 

9 

60.0 

57.0 

10 

66.3 

63.0 

11 

72.6 

69.0 

12 

78.9 

75.0 

13 

85.3 

81.0 

14 

, 01.6 

87.0 

15 

97.9 

93.0 

16 

104.2 

99.0 

17 

110.5 

105.0 

18 

lift Q 

111.0 

110. o 

19 


117.0 

20 





Log. M 

Log. P 

f 

1 

j 7.9947913 

8.1153289 

0 

.9947900 

4384 

1 

.9947888 

5479 

2 

75 

6575 

3 

62 

7670 

4 

49 

8767 

5 

37 

.1159865 

6 

24 

.1160962 

7 

.9947811 

2061 

8 

.9947798 

i 

3161 

9 

7.9947786 

8.1164261 

10 

73 

5361 

11 

60 

6463 

12 

48 

7565 

13 

35 

8668 

14 

22 

.1169772 

15 

.9947709 

.1170875 

16 

.9947697 

1980 

17 

84 

3085 

18 

71 

4191 

19 

7.9947658 

8.1175297 

20 

46 

6405 

21 

33 

7513 

22 

20 

8621 

23 

.9947607 

.1179730 

24 

♦ .9947594 

.1180840 

25 

82 

1951 

26 

69 

3061 

27 

56 

4174 

28 

43 

5286 

29 

7.9947531 

8.1186400 

30 

18 

7513 

31 

.9947505 

8627 

32 

.9947492 

.1189743 

33 

80 

.1190859 

34 

67 

1974 

35 

54 

3091 

36 

41 

4209 

37 

28 

5328 

38 

16 

6446 

39 

7.9947403 

8.1197566 

40 

.9947390 

8687 

41 

77 

.1199808 

42 

65 

.1200929 

43 

52 

2052 

44 

39 

3175 

45 

26 

4299 

46 

13 

5422 

47 

.9947301 

6547 

48 

.9947288 

7673 

49 

7.9947275 

8.1208800 

50 

62 

.1209926 

51 

49 

.1211054 

52 

37 

2182 

53 

24 

3310 

54 * 

.9947211 

4440 

55 

.9947198 

5571 

56 

85 

6702 

57 

73 

7833 

58 

60 

.1218965 

59 

7.9947147 

8.1220098 

60 


41 
















































































42 ° 


/ 

M 

P 

/ 

! 

l 


- 



0 

1 

2 

.0098790 

0 

0 

.0098790 

.0098789 

.0132437 

472 

506 

0 

1 

2 


P 

Interpolating Table. 

• 

3 

4 

541 

576 

610 

645 

680 

715 

3 

4 

Tabular Differences. 

diff. P 



34 

35 

36 

37 

5 

6 

9 

9 

5 

6 

// 

1.8 

// 

1.7 

// 

1.7 

n 

1.6 

0 

7 

8 

8 

7 

1 

1 

8 

5.3 

5.1 

5.0 

4.9 

8 

2 

9 

8 

749 

9 

8.8 

8.6 

8.3 

8.1 




3 

10 

.0098787 

.0132784 

10 

12.4 

12.0 

11.7 

11.4 


4 

11 

12 

13 

7 

819 

854 

889 

11 

15.9 

1 C A 

15.0 

14.6 


7 

12 

13 

ID .4: 

R 

19.4 

18.9 

18.3 

17.8 

o 

7 

6 

14 

6 

924 

14 

22.9 

22.3 

21.7 

21.1 


7 

15 


. 959 

15 

26.5 

25.7 

25.0 

24.3 

4 

6 

8 

16 

6 

0132994 

16 

30.0 

29.1 

28.3 

27.6 

17 

18 

5 

.0133029 

064 

17 

18 

9 

33.5 

32.6 

31.7 

30.8 

5 

10 

19 

5 

099 

19 

37.1 

36.0 

35.0 

34.1 


11 

20 

.0098785 

.0133134 

20 

40.6 

39.4 

38.3 

37.3 

12 

21 

4 

169 

21 

44.1 

42.9 

41.7 

40.5 

22 

23 

A 

205 

240 

22 

23 

13 


47.6 

46.3 

45.0 

43.8 

4 

14 

24 

3 

275 

24 

51.2 

49.7 

48.3 

47.0 


15 

25 


310 

25 

54.7 

53.1 

51.7 

50.3 

3 

16 

26 

3 

346 

26 

58.2 

56.6 

55.0 

53.5 

27 

28 

Q 

381 

416 

27 

28 

17 

o 

o 

61.8 

ah n 

58.3 

56.8 

2 

DU. U 

18 

29 

2 

452 

29 

65.3 

63.4 

61.7 

60.0 


19 

30 

.0098782 

.0133487 

30 

68.8 

66.9 

65.0 

63.2 

20 

31 

1 

523 

31 

79 4 

70 3 

AC 3 


32 

33 

i 

558 

594 

! 32 
i 33 


/ u . o 

DO. 0 

DD. O 

21 

X 

75.9 

73.7 

71 7 

69.7 

1 

4 1.1 

22 

34 

1 

629 

34* 

79.4 

77.1 

75.0 

73.0 





23 

35 

0 

665 

35 

82.9 

80.6 

78.3 

76.2 

24 

36 

0 

700 

36 

86.5 

84.0 

81.7 

79.5 

37 

38 

.0098780 

.0098779 

736 

772 

37 

38 

25 

90.0 

87.4 

85.0 

82.7 

26 

39 

9 

807 

39 

93.5 

90.9 

88.3 

85.9 





27 

40 

.0098779 

.0133843 

40 

97.1 

94.3 

91.7 

89.2 

28 

41 

8 

879 

41 

100.6 

97.7 

95.0 

92.4 

42 

43 

8 

8 

915 

951 

42 

43 

29 

104.1 

101.1 

98.3 

95.7 


44 

8 

.0133986 

44 

107.6 

104.6 

101.7 

98.9 

oU 





31 

A C 

7 

n-| Q/1 f\00 

45 

111.2 

108.0 

105.0 

102.2 

40 

46 

058 

32 

7 

46 

114.7 

111.4 

108.3 

105.4 

47 

48 

7 

094 

130 

47 

48 

33 

6 

118.2 

114.9 

111.7 

108.6 


49 

6 

166 

49 


118.3 

115.0 

111.9 

6*1 


• 




35 

50 

51 

.0098776 

.0134202 

50 



118.3 

115.1 



36 

6 

238 

51 




118.4 

52 

53 

5 

274 

311 

52 

53 




37 

5 





54 

5 

347 

54 

I 





55 

56 

57 

58 

59 

60 

4 

4 

4 

4 

3 

.0098773 

383 

419 

455 

492 

528 

.0134564 

55 

56 

57 

58 

59 

60 

j 







42 





































































































42 ° 


r 

Reciprocal 

M 

Reciprocal 

P 

0 

101.224 

75.508 

l 

5 

.488 

2 

5 

.468 

3 

5 

.448 

4 

6 

.429 

5 

6 

.409 

6 

6 

.389 

7 

7 

.369 

8 

7 

.350 

9 

7 

.330 

10 

101.227 

75.310 

11 

8 

.290 

12 

8 

.271 

13 

8 

.251 

14 

9 

.231 

15 

9 

.211 

16 

9 

.191 

17 

.229 

.172 

18 

.230 

.152 

19 

0 

.132 

20 

101.230 

75.112 

21 

1 

.092 

22 

1 

.073 

23 

1 

.053 

24 

2 

.033 

25 

2 

75.013 

' 26 

2 

74.993 

27 

2 

.973 

28 

3 

.953 

29 

3 

.933 

30 

101.233 

74.914 

31 

4 

.894 

32 

4 

.874 

33 

4 

.854 

34 

5 

.834 

35 

5 

.814 

36 

5 

.794 

37 

5 

.774 

38 

6 

.754 

39 

6 

.734 

40 

101.236 

74.714 

41 

7 

.694 

42 

7 

.674 

43 

7 

.654 

44 

8 

.634 

45 

8 

.614 

46 

8 

.594 

47 

8 

.574 

48 

9 

.554 

49 

9 

.534 

50 

101.239 

74.514 

51 

.240 

.494 

52 

0 

.474 

53 

0 

.454 

54 

1 

.434 

55 

1 

.414 

56 

1 

.394 

57 

1 

.374 

58 

2 

.354 

59 

2 

.334 

60 

101.242 

74.314 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

19 

20 

3.2 

3.0 

0 

1 

9.5 

9.0 

2 

15.8 

15.0 

3 

22.1 

21.0 

4 

28.4 

27.0 

5 

34.7 

33.0 

6 

41.1 

39.0 

7 

47.4 

45.0 

8 

53.7 

51.0 

9 

60.0 

57.0 

10 

66.3 

63.0 

11 

72.6 

69.0 

12 

78.9 

75.0 

13 

85.3 

81.0 

14 

91.6 

Q7 fi 

o/ . U 

15 

97.9 

93.0 

16 

104.2 

99.0 

17 

110.5 

105.0 

18 

116.8 

111.0 

19 


117.0 

20 





| 

i Log. M 

Log. P 

t 

7.9947147 

8.1220098 

0 

34 

1232 

1 

22 

2366 

2 

.9947109 

3501 

3 

.9947096 

4637 

4 

83 

5773 

5 

70 

6909 

6 

58 

8047 

7 

45 

.1229186 

8 

32 

.1230324 

9 

7.9947019 

8.1231464 

10 

.9947006 

2604 

11 

.9946994 

3745 

12 

81 

4886 

13 

68 

6029 

14 

55 

7172 

15 

42 

8316 

16 

30 

.1239459 

17 

17 

.1240604 

18 

.9946904 

1750 

19 

7.9946891 

8.1242897 

20 

78 

4043 

21 

65 

5191 

22 

53 

6339 

23 

40 

7488 

24 

27 

8638 

25 

14 

.1249788 

26 

.9946801 

.1250939 

27 

.9946789 

2090 

28 

76 

3243 

29 

7.9946763 

8.1254396 

30 

50 

5550 

31 

37 

6704 

32 

24 

7859 

33 

.9946712 

.1259015 

34 

.9946699 

.1260171 

35 

86 

1328 

36 

73 

2486 

37 

60 

3645 

38 

48 

4803 

39 

7.9946635 

8.1265963 

40 

22 

7124 

41 

.9946609 

8285 

42 

.9946596 

.1269446 

43 

83 

.1270609 

44 

71 

1773 

45 

58 

2936 

46 

45 

4101 

47 

32 

5266 

48 

19 

6432 

49 

7.9946506 

8.1277598 

50 

.9946494 

8766 

51 

81 

.1279934 

52 

68 

.1281102 

53 

55 

2271 

54 

42 

3442 

55 

29 

4613 

56 

17 

5783 

57 

.9946404 

6956 

58 

.9946391 

8129 

59 

7.9946378 

8.1289302 

60 


43 



































































43 ° 


/ 

M 

P 

f , 






0 

1 

2 

.0098773 

3 

2 

.0134564 

601 

637 

674 

710 

0 
• 1 

2 

o 

| 

P 

Interpolating Table. 


3 

4 

2 

2 

3 

4 

Tabular Differences. 

diff. P 

5 

1 

747 

5 

36 

37 

38 

39 

6 

1 

783 

820 

6 

rj 

// 

1.7 

// 

1.6 

// 

1.6 

// 

1.5 

0 

7 

1 


1 

8 

1 

856 

8 

5.0 

4.9 

4 7 

4.6 

Q 

0 

893 

9 

4./ | 

o 


8.3 

8.1 

7.9 

7.7 

& 

IQ 

.0098770 

.0134930 

10 

3 

11.7 

11.4 

H.l 1 

10.8 

11 

12 

.0098770 

.0098769 

.0134966 

.0135003 

11 

12 

4 

15.0 

14.6 

14.2 

! 13.8 

5 

13 

9 

040 

13 

18.3 

17.8 

17.4 1 

16.9 

14 

9 

077 

14 

6 


21.7 

21.1 

20.5 ! 

20.0 

15 

9 

113 

15 

7 

25.0 

24.3- 

23.7 

23.1 

16 

17 

8 

8 

150 

187 

16 

17 

8 

28.3 

27.6 

26.8 

26.2 

9 

18 

8 

224 

18 

31.7 

30.8 

30.0 

29.2 

19 

7 

261 

19 

10 


35.0 | 

34.1 

33.2 

32.3 

20 

.0098767 

.0135298 

20 

11 

38.3 

37.3 

36.3 

35.4 

21 

22 

7 

335 

372 

409 

21 

22 

12 

6 

41.7 

40.5 

39.5 

38 5 

13 

23 

6 

23 

45.0 

43.8 

42.6 

41.5 

24 

6 

446 

24 

Izt 


48.3 ! 

! 47 0 

1 ■ 

‘ oo 

to 

44.6 


25 


483 

25 

15 

6 

51.7 

! 50.3 

48.9 

47.7 

26 

5 

521 

26 

16 

27 

28 

5 

558 

595 

27 

55.0 ; 

53.5 

52.1 

50.8 

17 

5 

28 

58.3 

56.8 

55.3 

53.8 

29 

4 

632 

29 

18 


61.7 

60.0 

58.4 

56.9 

30 

.0098764 

.0135670 

30 

19 

65.0 

63.2 

61.6 

60.0 

31 

4 

707 

31 

20 

32 

33 

A 

744 

782 

32 

33 

68.3 

66.5 

64.7 

63.1 

o 

21 

3 

71.7 

69.7 

67.9 

66.2 

34 

3 

819 

34 

22 


, 75.0 

73.0 

71.1 

69.2 

35 

o 

857 

35 

23 

3 

78.3 

76.2 

74 2 ' 

72.3 

36 

2 

894 

36 

24 

37 

38 

2 

qqo 

.0135969 

37 

38 

81.7 

79.5 

77.4 

’ 75.4 

La 

o 

25 


85.0 

82.7 

80.5 

78.5 

39 

2 

.0136007 

39 

26 


88.3 

| 

85.9 

83 7 

81.5 

40 

.0098761 

.0136044 

40 

27 

91.7 

89.2 

86.8 ’ 

| 84.6 

41 

1 

082 

41 

OQ 

42 

43 

1 

120 

157 

42 

43 

95.0 

92.4 

90.0 

87.7 

LO 

jL 

0 

90 

98.3 

95.7 

93.2 

90.8 


44 

0 

195 

44 

30 





101.7 

98.9 

96.3 

93.8 

45 

.0098760 

233 

45 

91 

105.0 

102.2 

99.5 

96.9 

ul 

46 

.0098759 

271 

46 

99 

47 

48 

9 

309 

347 

47 

48 

108.3 

105.4 

102.6 

100.0 

oL 

9 

99 

111.7 

108.6 

105.8 

103.1 

oo 

49 

9 

384 

49 

34 





115.0 

111.9 

108.9 

106.2 

50 

.0098758 

8 

.0136422 

50 

35 

118.3 

115.1 

112.1 

109.2 

51 

460 

51 

36 

52 

8 

498 

536 

575 

52 

53 | 

54 


118.4 

115.3 

112.3 

53 

54 

7 

7 


37 



118.4 

115.4 



38 




1 




118.5 

55 

56 

7 

7 

613 

651 

689 

727 

765 

.0136804 

55 , 

56 1 

57 

58 

59 

60 

1 




39 





57 

58 

59 

60 

i 6 

■6 

6 

.0098755 



44 







































































































































43 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.242 

74.314 

1 

3 

.294 

2 

3 

.274 

3 

3 

.254 

4 

4 

.233 

5 

4 

.213 

6 

4 

.193 

7 

4 

.173 

8 

5 

.153 

9 

5 

.133 

10 

101.245 

74.113 

11 

6 

.093 

12 

6 

.072 

13 

6 

.052 

14 

7 

.032 

15 

7 

74.012 

16 

7 

73.992 

17 

7 

. .971 

18 

8 

.951 

19 

8 

.931 

20 

101.248 

73.911 

21 

9 

.891 

22 

9 

.870 

23 

.249 

.850 

24 

.250 

.830 

25 

0 

.810 

26 

0 

.790 

27 

0 

.769 

28 

1 

.749 

29 

1 

.729 

30 

101.251 

73.708 

31 

2 

.688 

32 

2 

.668 

33 

2 

.648 

34 

3 

.627 

35 

3 

.607 

36 

3 

.587 

37 

3 

.566 

38 

4 

.546 

39 

4 

.526 

40 

101.254 

73.505 

41 

5 

.485 

42 

5 

.465 

43 

5 

.444 

44 

6 

.424 

45 

6 

.404 

46 

6 

.383 

47 

6 

.363 

48 

7 

.343 

49 

7 

.322 

50 

101.257 

73.302 

51 

8 

.281 

52 

8 

.261 

53 

8 

.241 

54 

9 

.220 

55 

9 

.200 

56 

9 

.179 

57 

.259 

.159 

58 

.260 

.138 

59 

0 

.118 

60 

101.260 

73.097 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

20 

21 

ft 

3.0 

n 

2 9 

0 

1 

9.0 

8.6 

2 

15.0 

14.3 

3 

21.0 

20.0 

4 

27.0 

25.7 

5 

33.0 

31.4 

6 

39.0 

37.1 

7 

45.0 

42.9 

8 

51.0 

48.6 

9 

57.0 

54.3 

10 

63.0 

60.0 

11 

69.0 

65.7 

12 

75.0 

71.4 

13 

81.0 

77.1 

14 

87.0 

82.9 

15 

93.0 

88.6 

16 

99.0 

94.3 

17 

105.0 

100.0 

18 

111.0 

105.7 

19 

117.0 

111.4 

20 


117.1 

21 





Log. M 

Log. P 

r 

7.9946378 

8.1289302 

0 

65 

.1290476 

t 

53 

1651 

z 

40 

2,827 

3 

27 

4002 

4 

14 

5179 

5 

.9946301 

6357 

6 

.9946288 

7536 

i T 

75 

8714 

8 

63 

.1299894 

9 

7.9946250 

8.1301074 

10 

37 

2255 

11 

24 

3437 

12 

.9946211 

4619 

13 

.9946198 

5803 

14 

86 

6986 

IS 

73 

8170 

16 

60 

.1309356 

IT 

47 

.1310541 

18 

34 

1728 

19' 

7.9946121 

8.1312915 

20^ 

.9946108 

4104 

21 

.9946096 

5292 

22" 

83 

6481 

23 

70 

7671 

24 

57 

.1318862 

25. 

44 

.1320053 

26; 

31 

1246 

27 

18 

2439 

28 

.9946006 

3631 

29 

7.9945993 

8.1324826 

30 

80 

6021 

31 

67 

7217 

32 

54 

8413 

33 

41 

.1329610 

34 

29 

.1330808 

35 

16 

2006 

36 

.9945903 

3205 

37 

.9945890 

4405 

38 

77 

5606 

39 

7.9945864 

8.1336806 

40 

51 

8008 

41 

39 

.1339211 

42 

26 

.1340414 

43 

13 

1618 

44 

.9945800 

2823 

45 

.9945787 

4029 

46 

74 

5234 

47 

61 

6442 

48 

49 

7649 

49 

7.9945736 

8.1348857 

50 

23 

.1350066 

51 

.9945710 

1276 

52 

.9945697 

2487 

53 

84 

3697 

54. 

71 

4909 

55 

59 

6122 

56. 

46 

7334 

57 

33 

8549 

58- 

20 

.1359763 

59 

7.9945607 

8.1360979 

60 


45 















































































44 ° 


f 

M 

0 

.0098755 

1 

5 

2 

5 

3 

5 

4 

4 

5 

4 

6 

4 

7 

3 

8 

3 

3 

3 

10 

.0098752 

11 

2 

12 

2 

13 

2 

14 

1 

15 

1 

16 

1 

17 

0 

18 

0 

19 

0 

20 

.0098750 

21 

.0098749 

22 

9 

23 

9 

24 

8 

25 

8 

26 

8 

27 

7 

28 

7 

29 

7 

30 

.0098747 

31 

6 

32 

6 

33 

6 

34 

5 

35 

5 

36 

5 

37 

5 

38 

4 

39 

4 

40 

.0098744 

41 

3 

42 

3 

43 

3 

44 

3 

45 

2 

46 

2 

47 

2 

48 

1 

49 

1 

.50 

.0098741 

51 

0 

.52 

0 

53 

0 

54 

.0098740 

.55 

.0098739 

56 

9 

.57 

9 

58 

8 

59 

8 

60 

.0098738 


P 

/ 

.0136804 

0 

842 

1 

880 

2 

919 

3 

957 

, 4 

i 

.0136996 

5 

.0137034 

6 

073 

7 

111 

8 

150 

9 

.0137188 

10 

227 

11 

266 

12 

304 

13 

343 

14 

382 

15 

421 

16 

460 

17 

498 

18 

537 

19 

.0137576 

20 

615 

21 

654 

22 

693 

23 

732 

24 

771 

25 

811 

26 

850 

27 

889 

28 

928 

29 

.0137968 

30 

.0138007 

31 

046 

32 

086 

33 

125 

34 

165 

35 

204 

36 

244 

37 

283 

38 

323 

39 

.0138362 

40 

402 

41 

442 

42 

481 

43 

521 

44 

561 

45 

601 

46 

641 

47 

681 

48 

721 

49 

.0138761 

50 

801 

51 

841 

52 

881 

53 

921 

54 

.0138961 

55 

.0139001 

56 

• 041 

57 

082 

58 

122 

59 

.0139162 

60 


i 


P 

Interpolating Table. 


Tabular Differences. 

- diff. P 

38 

39 

40 

41 

1.6 

ft 

1.5 

// 

1.5 

ft 

1.5 

0 

1 

4.7 

4.6 

4.5 

4.4 

1 

- 2 

7.9 

7.7 

7.5 

7.3 

3 

11.1 

10.8 

10.5 

10.2 

4 

14.2 

13.8 

13.5 

13.2 

5 

17.4 

16.9 

16.5 

16.1 

6 

20.5 

20.0 

19.5 

19.0 

7 

23.7 

23.1 

22.5 

22.0 

8 

26 r8 

o a o 

1 OK K 

24.9 

6\J.6 . 6xJ.U 

9 

30.0 

on o no c 

27.8 

6 O . 6 

i 60 .u 

10 

33.2 

32.3 

1 31.5 

30.7 

11 

36.3 

35.4 

34.5 

33.7 

12 

QQ K 

QQ K 

Q7 ^ 


. 0 

OO .0 

Of.o 

oO . D 

13 

42.6 

41.5 

40.5 

39.5 

14 

45.8 

44.6 

43.5 

42.4 

15 

48.9 

47.7 

46.5 

45.4 

16 

52.1 

50.8 

49.5 

48.3 

17 

55.3 

53.8 

52.5 

51.2 

18 

58.4 

56.9 

55.5 

54.1 

19 

61.6 

60.0 

58.5 

57.1 

20 

64.7 

63.1 

61.5 

60.0 

21 

67.9 

66.2 

64.5 

62.9 

22 

71.1 

69.2 

67.5 

65.9 

23 

7 a o 

79 Q 

70.5 

68.8 


/ 6 .0 

24 

77 A 

75.4 

73.5 

71,7 

25 

80.5 

78.5 

76.5 

74.6 

26 

83.7 

81.5 

79.5 

77.6 

27 

86.8 

84.6 

82.5 

80.5 

28 

90.0 

87.7 

85.5 

83.4 

29 

30 

93.2 

90.8 

88.5 

86.3 


93.8 

Q1 5 

89.3 ■ 

yo . o 


31 

99.5 

96.9 

94.5 

92.2 - 

32 

102.6 

100.0 

97.5 

95.1 - 

33 

105.8 

103.1 

100.5 

98.0 - 

34 

108.9 

106.2 

103.5 

101.0 - 

35 

112.1 | 109.2 

106.5 

103.9 - 

36 

115.3 | 112.3 

109.5 

106.8 - 

37 

118.4 j 115.4 

112.5 

109.8 - 

38 

.| 118.5 

115.5 

119 7 

11 6.1 

39 

j 

118.5 | 115.6 

40 

i 



l 

11 Q K 

1 lo. 0 

41 



. 1 


46 

















































































































































44 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 




Log. M 

Log. P 

/ 

0 

101.260 

73.097 




7.9945607 

8.1360979 

0 

1 

1 

.077 




.9945594 

2194 

1 

2 

1 

.057 




81 

3411 

2 

3 

1 

.036 




69 

4629 

3 

4 

2 

73.016 




56 

5847 

4 

5 

2 

72.995 




43 

7066 

5 

6 

2 

.975 




30 

8286 

6 

7 

2 

.954 




17 

.1369505 

7 

8 

3 

.934 




.9945504 

.1370727 

8 

9 

3 

.913 




.9945491 

1949 

9 

10 

101.263 

72.893 




7.9945478 

8.1373171 

10 

11 

4 

.872 




65 

4394 

11 

12 

4 

.851 




53 

5618 

12 

13 

14 

4 

5 

.831 

.810 

Reciprocal -r 

Interpolating Table. 

40 

27 

6843 

8068 

13 

14 

15 

16 

5 

.790 

Tabular Diff. 

diff. 

frtrv P 

14 

.1379294 

15 

5 

.769 

20 

21 

rep. x 

.9945401 

.1380521 

16 

17 

5 

.749 


.9945388 

1748 

17 





18 

6 

.728 

// 

n 

0 

76 

2976 

18 

19 

6 

.708 

3.0 

2.9 

1 

63 

4205 

19 

20 

101.266 

72.687 

9.0 

8.6 

7.9945350 

8.1385435 

20 

2 

15.0 

14.3 

21 

7 

.666 

Q 

37 

6666 

21 

22 

7 

.646 


20.0 

O 

24 

7896 

22 

7 


A 

23 

.625 


.9945311 

.1389128 

23 

27.0 

25.7 

T 

24 

8 

.605 

K 

.9945298 

.1390361 

24 




33.0 

31.4 

D 




25 

8 

.584 



A 

86 

1593 

25 

39.0 

37.1 

O 

26 

8 

.563 

7 

73 

2827 

26 

27 

28 

8 

9 

.543 

.522 

45.0 

42.9 

60 

47 

4062 

5298 

27 

28 

8 

51.0 

48.6 

29 

9 

.501 

9 

34 

6533 

29 

30 

101.269 

72.481 

57.0 

54.3 

7.9945221 

.9945208 

8.1397770 

30 

10 

£9 A 

AA A 

31 

.270 

.460 

Do .U 

OU. U 

11 

.1399008 

31 

32 

0 

440 

AQ n 

A* 7 

.9945195 

.1400246 

32 

33 

0 

.419 

oy .u 


12 

83 

-1485 

33 

75.0 

71.4 

34 

1 

.398 

13 

70 

2725 

34 




qi a 

77.1 




35 

1 

.377 

ol .U 

14 

57 

3965 

35 




36 

1 

.357 

87.0 

82.9 

15 

44 

5206 

36 

37 

38 

1 

2 

.336 

.315 

93.0 

88.6 

31 

18 

6448 

7691 

37 

38 

16 



39 

2 

.295 

99.0 

94.3 

17 

18 

.9945105 

.1408934 

39 

40 

101.272 

72.274 

105.0 

100.0 

7.9945093 

8.1410178 

40 



41 

3 

.253 

111.0 

105.7 

19 

80 

1423 

41 

42 

43 

3 

233 

117 A 

111 A 

67 

2668 

42 

3 

.212 

117.U 

111.4 

20 

54 

3915 

43 


117.1 

A A 

4 

.191 

--—--- 

41 

' 5162 

44 



21 

45 

A 

.170 



28 

6410 

45 

4 




46 

4 

.150 




15 

7657 

46 

47 

4 

.129 




.9945002 

.1418907 

47 

48 

5 

.108 




.9944990 

.1420157 

48 

49 

5 

.087 




77 

1407 

49 

50 

101.275 

72.067 




7.9944964 

8.1422659 

50 

51 

6 

.046 




51 

3911 

51 

52 

6 

.025 




38 

5164 

52 

53 

6 

72.004 




25 

6417 

53 

54 

7 

71.983 




.9944912 

7.671 

54 

55 

7 

.963 




.9944899 

. 1428927 

55 

56 

7 

.942 




87 

.1430182. 

56 

57 

7 

.921 




74 

1438 

57 

58 

8 

.900 




61 

2696 

58 

59 

8 

.879 




48 

3954 

59 

60 

101.278 

71.859 




7.9944835 

8.1435212 

60 


47 






























































45 ° 


P 

Interpolating Table. 


/ 

M 

i 

P 

f 

0 

.0098738 

.0139162 

0 

1 

8 

203 

1 

2 

7 

243 

2 

3 

7 

283 

3 

4 

7 

324 

4 

1 

-5 

6 

364 

5 

6 

6 

405 

6 

-'7 

6 

445 

7 

$ 

5 

486 

8 


5 

527 

9 

10 

.0098735 

.0139567 

10 

11 

5 

608 

11 

12 

' 4 

649 

12 

13 

4 

690 

13 

14 

4 

730 

14 

15 

3 

771 

15 

16 

3 

812 

16 

17 

3 

853 

17 

18 

3 

894 

18 

19 

2 

935 

19 

20 

.0098732 

.0139976 

20 | 

21 

2 

.0140017 

21 

22 

1 

058 

22 

23 

1 

099 

23 

24 

1 

141 

24 

25 

1 

182 

25 

26 

0 

223 

26 

27 

0 

264 

27 

. :28 

.0098730 

306 

28 

29 

.0098729 

347 

29 

'30 

.0098729 

.0140389 

30 

31 

9 

430 

31 

32 

8 

471 

32 

33 

8 

513 

33 

24 

8 

554 

34 

35 

8 

596 

35 

36 

7 

638 

36 

37 

7 

679 

37 

38 

7 

721 

38 

39 

6 

763 

39 

40 

.0098726 

.0140805 

40 

41 

6 

846 

41 

42 

6 

888 

42 

43 

5 

930 

43 

44 

5 

i 

.0140972 

44 

45 

5 

.0141014 

45 

46 

4 

056 

46 

47 

4 

098 

47 

48 

4 

140 

48 

49 

4 

182 

49 

.50 

.0098723. 

.0141224 

50 

51 

3 

266 

51 

52 

3 

309 

52 

53 

2 

351 

53 

54 

2 

393 

54 

55 

2 

435 

55 

56 

1 

478 

56 

57 

1 

520 

57 

58 

1 

563 

58 

59 

1 

605 

59 

60 

.0098720 

.0141648 

60 


Tabular Differences. 


40 

41 

42 

43 

tt 

1.5 

// 

1.5 

// 

1.4 

n 

1.4 

4.5 

4.4 

4.3 

4.2 

7.5 

7.3 

7.1 

7.0 

10.5 

10.2 

10.0 

9.8 

13.5 

13.2 

12.9 

12.6 

16.5 

16.1 

15.7 

15.3 

19.5 

19.0 

18.6 

18.1 

22.5 

22.0 

21.4 

20.9 

25.5 

24.9 

24.3 

23.7 

28.5 

27.8 

27.1 

26.5 

31.5 

30.7 

30.0 

29.3 

34.5 

33.7 

32.9 

32.1 

37.5 

36.6 

35.7 

34.9 

40.5 

39.5 

38.6 

37.7 

43.5 

42.4 

41.4 

40.5 - 

46.5 

45.4 

44.3 

43.3 - 

49.5 

48.3 

47.1 

46.0 - 

52.5 

51.2 

50.0 

48.8 - 

55.5 

54.1 

52.9 

51.6 - 

58.5 

57.1 

55.7 

54.4 - 

61.5 

60.0 

58.6 

57.2 - 

64.5 

62.9 

61.4 

60.0 - 

67.5 

65.9 

64.3 

62.8 - 

70.5 

68.8 

67.1 

65.6 - 

73.5 

71.7 

70.0 

68.4 - 

76.5 

74.6 

72.9 

71.2 - 

79.5 

77.6 

75.7 

74.0 - 

82.5 

80.5 

78.6 

76.7 - 

85.5 

83.4 

81.4 

79.5 - 

88.5 

86.3 

84.3 

82.3 - 

91.5 

89.3 

87.1 

85.1 - 

94.5 

92.2 

90.0 

87.9 - 

97.5 

95.1 

92.9 

90.7 

100.5 

98.0 

95.7 

93.5 - 

103.5 

101.0 

98.6 

96.3 - 

106.5 

103.9 

101.4 

99.1 - 

109.5 

106.8 

104.3 

101.9 - 

112.5 

109.8 

107.1 

104.7 - 

115.5 

112.7 

110.0 

107.4 - 

118.5 

115.6 

112.9 

110.2 - 


118.5 • 

115.7 

113.0 - 



118.6 

115.8 - 






118.6 - 









diff.P 

0 

1 


9 

10 


11 

12 


13 

14 


15 

16 


17 

18 


19 


20 


21 

22 


23 

24 


25 

26 
27 


28 

29 


30 

31 

32 


33 

34 


35 

36 

37 

38 

39 

40 

41 

42 

43 


48 


















































































































































45 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.278 

71.859 

X 

9 

.838 

2 

9 

.817 

3 

.279 

.796 

4 

.280 

.775 

5 

0 

.754 

6 

0 

.734 

7 

0 

.713 

8 

1 

.692 

9 

1 

.671 

10 

101.281 

71.650 

11 

2 

.629 

12 

2 

.608 

13 

2 

.587 

14 

3 

.566 

15 

3 

.545 

16 

3 

.525 

17 

3 

.504 

18 

4 

.483 

19 

4 

.462 

20 

101.284 

71.441 

21 

5 

.420 

22 

5 

.399 

23 

5 

.378 

24 

6 

.357 

25 

6 

.336 

26 

6 

.315 

27 

6 

.294 

28 

7 

.273 

29 

7 

.252 

30 

101.287 

71.231 

31 

8 

.210 

32 

8 

.189 

33 

8 

.168 

34 

9 

.147 

35 

9 

.126 

36 

9 

.105 

37 

.289 

.084 

38 

.290 

.063 

39 

0 

.042 

40 

101.290 

71.020 

41 

1 

70.999 

42 

1 

.978 

43 

1 

.957 

44 

2 

.936 

45 

2 

.915 

46 

2 

.894 

47 

2 

.873 

48 

3 

.852 

49 

3 

.831 

50 

101.293 

70.809 

51 

4 

.788 

52 

4 

.767 

53 

4 

.746 

54 

5 

.725 

55 

5 

.704 

56 

5 

.682 

57 

5 

.661 

58 

6 

.640 

59 

6 

.619 

60 

101.296 

70.598 


Reciprocal P 
Interpolating Table. 


Tabular Differences. 

diff. 
rep. P 

20 

21 

22 

// 

3.0 

' // 

2.9 

n 

2.7 

0 

1 

9.0 

8.6 

8.2 

2 

15.0 

14.3 

13.6 

3 

21.0 

20.0 

19.1 

4 

27.0 

25.7 

24.5 

5 

33.0 

31.4 

30.0 

6 

39.0 

37.1 

35.5 

7 

45.0 

42.9 

40.9 

8 

51.0 

48.6 

46.4 

9 

57.0 

54.3 

51.8 

10 

63.0 

60.0 

57.3 

11 

69.0 

65.7 

62.7 

12 

75.0 

71.4 

68.2 

13 

81.0 

77.1 

73.6 

14 

87.0 

82.9 

79.1 

15 

93.0 

88.6 

84.5 

16 

99.0 

94.3 

90.0 

17 

105.0 

100.0 

95.5 

18 

111.0 

105.7 

100.9 

19 

117.0 

111.4 

106.4 

20 


117.1 

111.8 

21 




117.3 

22 








Log. M 

Log. P 

f 

7.9944835 

8.1435212 

0 

22 

6472 

1 

.9944809 

7732 

2 

.9944797 

.1438992 

3 

84 

.1440254 

4 

71 

1517 

5 

58 

2779 

6 

45 

4043 

7 

32 

5308 

8 

19 

6574 

9 , 

7.9944706 

8.1447839 

10 

.9944694 

.1449106 

11 

81 

.1450374 

12 

68 

1641 

13 

55 

2911 

14 

42 

4181 

15 

29 

5451 

16 

17 

6722 

17 

.9944604 

7994 

18 

.9944591 

.1459267 

19 

7.9944578 

8.1460540 

20 

65 

1814 

21 

52 

3089 

22 

39 

4365 

23 

26 

5641 

24 

14 

6919 

25 

.9944501 

8197 

26 

.9944488 

. 1469475 

27 

75 

.1470754 

28 

62 

2035 

29 

7.9944449 

8.1473316 

30 

36 

4597 

31 

23 

5880 

32 

.9944410 

7163 

33 

.9944398 

8446 

34 

85 

.1479731 

35 

72 

.1481017 

36 

59 

2303 

37 

46 

3589 

38 

33 

4877 

39 

7.9944320 

8.1486166 

40 

.9944307 

7454 

41 

.9944295 

.1488745 

42 

82 

. 1490036 

43 

69 

1327 

44 

56 

2619 

45 

43 

3912 

46 

30 

5206 

47 

18 

6500 

48 

.9944205 

7795 

49 

7.9944192 

8.1499090 

50 

79 

.1500387 

51 

66 

1685 

52 

53 

2984 

53 

40 

4282 

54 

27 

5582 

55 

15 

6883 

56 

.9944102 

8184 

57 

.9944089 

.1509485 

58 

76 

.1510788 

59 

7.9944063 

8.1512092 

60 


49 












































































46 ° 


P 

Interpolating Table. 


/ 

M 

P 

/ 

0 

.0098720 

.0141648 

0 

1 

0 

690 

1 

2 

.0098720 

733 

2 

3 

.0098719 

775 

3 

4 

9 

. 818 

4 

5 

9 

861 

5 

6 

9 

903 

6 

7 

8 

946 

7 

8 

8 

.0141989 

8 

9 

8 

.0142032 

9 

10 

.0098717 

.0142075 

10 

11 

7 

118 

11 

12 

7 

161 

12 

13 

6 

204 

13 

14 

6 

247 

14 

15 

6 

290 

15 

16 

6 

333 

16 

17 

5 

376 

17 

18 

5 

419 

18 

19 

5 

462 

19 

20 

.0098714 

.0142506 

20 

21 

4 

549 

21 

22 

4 

592 

22 

23 

4 

636 

23 

24 

3 

679 

24 

25 

3 

723 

25 

26 

3 

766 

26 

27 

2 

810 

27 

28 

2 

853 

28 

29 

2 

897 

29 

30 

.0098711 

.0142941 

30 

31 

1 

.0142984 

31 

32 

1 

.0143028 

32 

33 

1 

072 

33 

34 

0 

116 

34 

35 

0 

159 

35 

36 

.0098710 

203 

36 

37 

.0098709 

247 

37 

38 

9 

291 

38 

39 

9 

335 

39 

40 

.0098709 

.0143379 

40 

41 

8 

423 

41 

42 

8 

467 

42 

43 

8 

512 

43 

44 

7 

556 

44 

45 

7 

600 

45 

46 

7 

644 

46 

47 

7 

689 

47 

48 

6 

733 

48 

49 

6 

777 

49 

50 

' .0098706 

.0143822 

50 

51 

5 

866 

51 

52 

5 

911 

52 

53 

5 

.0143955 

53 

54 

4 

.0144000 

54 

55 

4 

045 

55 

56 

4 

089 

56 

57 

4 

134 

57 

58 

3 

179 

58 

59 

3 

224 

59 

60 

.0098703 

.0144269 

60 


Tabular Differences. 


42 

43 

44 

45 

■ am . j 

n 

1.4 

n 

1.4 

n 

1.4 

n 

1.3 

0 

i 

4.3 

4.2 

4.1 

4.0 

2 

7.1 

7.0 

6.8 

6.7 

3 

10.0 

9.8 

9.5 

9.3 

4 

12.9 

12.6 

12.3 

12.0 

5 

15.7 

15.3 

15.0 

14.7 

6 

18.6 

18.1 

17.7 

17.3 

7 

21.4 

20.9 

20.5 

20.0 

8 

24.3 

23.7 

23.2 

22.7 

9 

27 . 1 . 

26.5 

25.9 

25,3 

10 

30.0 

29.3 

28.6 

28.0 

11 

32.9 

32.1 

31.4 

30.7 

12 

35.7 

34.9 

34.1 

33.3 

13 

38.6 

37.7 

36.8 

36.0 

14 

41.4 

40.5 

39.5 

38.7 

15 

44.3 

43.3 

42.3 

41.3 

16 

47.1 

46.0 

45.0 

44.0 

17 

50.0 

48.8 

47.7 

46.7 

18 

52.9 

51.6 

50.5 

49.3 

19 

55.7 

54.4 

53.2 

52.0 

20 

58.6 

57.2 

55.9 

54.7 

21 

61.4 

60.0 

58.6 

57.3 

22 

64.3 

62.8 

61.4 

60.0 

23 

67.1 

65.6 

64.1 

62.7 

24 

70.0 

68.4 

66.8 

65.3 

25 

72.9 

71.2 

69.5 

68.0 

26 

27 

75.7 

74.0 

72.3 

70.7 

78.6 

76.7 

75.0 

73.3 

28 

81.4 

79.5 

77.7 

76.0 

29 

84.3 

82.3 

80.5 

78.7 

30 

87.1 

85.1 

83.2 

81.3 

31 

90.0 

87.9 

85.9 

84.0 

32 

92.9 

90.7 

88.6 

86.7 

33 

95.7 

93.5 

91.4 

89.3 

34 

98.6 

96.3 

94.1 

92.0 

35 

101.4 

99.1 

96.8 

94.7 

36 

104.3 

101.9 

99.5 

97.3 

37 

107.1 

104.7 

102.3 

100 . 0 , 

38 

110.0 

107.4 

105.0 

102.7 

39 

112.9 

110.2 

107.7 

105.3 

40 

115.7 

113.0 

110.5 

108.0 

41 

118.6 

115.8 

113.2 

110.7 

42 


118.6 

115.9 

113.3 

43 




118.6 

116.0 

44 






118.7 

45 









50 










































































































































46 ° 


/ 

Reciprocal 

M 

Reciprocal 

P 

0 

101.296 

70.598 

1 

7 

.577 

2 

7 

.555 

3 

7 

.534 

4 

8 

.513 

5 

8 

.492 

6 

8 

.470 

7 

8 

.449 

8 

9 

.428 

9 

9 

.407 

10 

101.299 

70.385 

11 

.300 

.364 

12 

0 

.343 

13 

0 

.322 

14 

1 

.300 

15 

1 

.279 

16 

1 

.258 

17 

1 

.237 

18 

2 

.215 

19 

2 

.194 

20 

101.302 

70.173 

21 

3 

.151 

22 

3 

.130 

23 

3 

.109 

24 

4 

.087 

25 

4 

.066 

' 26 

4 

.045 

27 

4 

.023 

28 

5 

70.002 

29 

5 

69.981 

30 

101.305 

69.959 

31 

6 

.938 

32 

6 

.916 

33 

6 

.895 

34 

7 

.874 

35 

7 

.852 

36 

7 

.831 

37 

7 

.809 

38 

8 

.788 

39 

8 

.767 

40 

101.308 

69.745 

41 

9 

.724 

42 

9 

.702 

43 

.309 

.681 

44 

.310 

.659 

45 

0 

.638 

46 

0 

.616 

47 

0 

.595 

48 

1 

.573 

49 

1 

.552 

50 

101.311 

69.530 

51 

2 

.509 

52 

2 

.487 

53 

2 

.466 

54 

3 

.444 

55 

3 

.423 

56 

3 

.401 

57 

3 

.380 

58 

4 

.358 

59 

4 

.337 

60 

101.314 

69.315 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

21 

22 

// 

2.9 

// 

2.7 

0 

1 

8.6 

8.2 

2 

14.3 

13.6 

3 

20.0 

19.1 

4 

25.7 

24.5 

5 

31.4 

30.0 

e 

37.1 

35.5 

7 

42.9 

40.9 

8 

48.6 

46.4 

9 

54.3 

51.8 

10 

60.0 

57.3 

11 

65.7 

62.7 

12 

71.4 

68.2 

13 

77.1 

73.6 

14 

82.9 

79.1 

15 

88.6 

84.5 

16 

94.3 

90.0 

17 

100.0 

95.5 

18 

105.7 

100.9 

19 

111.4 

106.4 

20 

117.1 

111.8 

21 


117.3 

22 





Log. M 

Log. P 

f 

7.9944063 

8.1512092 

0 

50 

3397 

1 

37 

4701 

2 

25 

6007 

3 

.9944012 

7314 

4 

.9943999 

8621 1 

f 5 

86 

.1519929 1 

6 

73 

.1521238 I 

7 • 

60 

2548 

8 

47 

3858 

9 

7.9943934 

8.1525169 

10 

22 

6482 

11 

.9943909 

7794 

12 

.9943896 

.1529107 

13 

83 

.1530422 

14 

70 

1737 

15 

57 

3052 

16 

44 

4369 

17 

32 

5687 

18 

19 

7004 

19 

7.9943806 

8.1538323 

20 

.9943793 

.1539643 

21 

80 

.1540964 

22 

67 

2284 

23 

54 

3606 

24 

42 

4929 

25 

29 

6252 

26 

16 

7577 

27 

.9943703 

.1548902 

28 

.9943690 

.1550228 

29 

7.9943677 

8.1551554 

30 

64 

2882 

31 

52 

4210 

32 

39 

5538 

33 

26 

6868 

34 

13 

8199 

35 

.9943600 

.1559530 

36 

.9943587 

.1560862 

37 

75 

2195 

38 

62 

3529 

39 

7.9943549 

8.1564862 

40 

36 

6198 

41 

23 

7534 

42 

.9943510 

.1568871 

43 

.9943497 

.1570208 

44 

85 

1546 

45 

72 

2886 

46 

59 

4225 

47 

46 

5566 

48 

33 

6907 

49 

7.9943420 

8.1578250 

50 

.9943407 

.1579592 

51 

.9943395 

.1580936 

52 

82 

2281 

53 

69 

3626 

54 

56 

4972 

55 

43 

6319 

56 

30 

7667 

57 

18 

.1589015 

58 

.9943305 

.1590364 

59 

7.9943292 

8.1591715 

60 


51 








































































47 ( 


Interpolating Table. 


/ 

M 

P 

/ 

0 

.0098703 

.0144269 

0 

1 

2 

313 

1 

2 

2 

358 

2 

3 

2 

403 

3 

4 

2 

448 

4 

5 

1 

493 

5 

6 

1 

538 

6 

7 

1 

583 

7 

8 

0 

629 

8 

9 

0 

674 

9 

10 

.0098700 

.0144719 

10 

11 

.0098700 

764 

11 

12 

.0098699 

810 

12 

13 

9 

855 

13 

14 

9 

901 

14 

15 

8 

946 

15 

16 

8 

.0144991 

16 

17 

8 

.0145037 

17 

18 

7 

083 

18 

19 

7 

128 

19 

20 

.0098697 

.0145174 

20 

21 

7 

219 

21 

22 

6 

265 

22 

23 

6 

311 

23 

24 

6 

357 

24 

25 

5 

403 

25 

26 

5 

449 

26 

27 

5 

495 

27 

28 

5 

541 

28 

29 

4 

587 

29 

30 

.0098694 

.0145633 

30 

31 

4 

679 

31 

32 

3 

725 

32 

33 

3 

771 

33 

34 

3 

817 

34 

35 

3 

864 

35 

36 

2 

910 

36 

37 

2 

.0145956 

37 

38 

2 

.0146003 

38 

39 

1 

049 

39 

40 

.0098691 

.0146096 

40 

41 

1 

142 

41 

42 

1 

189 

42 

43 

0 

235 

43 

44 

0 

282 

44 

45 

.0098690 

329 

45 

46 

.0098689 

375 

46 

47 

9 

422 

47 

48 

9 

469 

48 . 

49 

8 

516 

49 

50 

.0098688 

.0146563 

50 

51 

8 

610 

51 

52 

8 

657 

52 

53 

7 

704 

53 

54 

7 

751 

54 

55 

7 

798 

55 

56 

6 

845 

56 

57 

6 

892 

57 

58 

6 

940 

58 

59 

6 

.0146987 

59 

60 

.0098685 

.0147034 

60 


Tabular Differences. 


44 

45 

46 

47 

48 

n 

// 

n 

// 

n 

1.4 

1.3 

1.3 

1.3 

1.25 

4.1 

4.0 

3.9 

3.8 

3.75 

6.8 

6.7 

6.5 

6.4 

6.25 

9.5 

9.3 

9.1 

8.9 

8.75 

12.3 

12.0 

11.7 

11.5 

11.25 

15.0 

14.7 

14.3 

14.0 

13.75 

17.7 

17.3 

17.0 

16.6 

16.25 

20.5 

20.0 

19.6 

19.1 

18.75 

23.2 

22.7 

22.2 

21.7 

21.25 

25.9 

25.3 

24.8 

24.3 

23.75 

28.6 

28.0 

27.4 

26.8 

26.25 

31.4 

30.7 

30.0 

29.4 

28.75 

34.1 

33.3 

32.6 

31.9 

31.25 

36.8 

36.0 

35.2 

34.5 

33.75 

39.5 

38.7 

37.8 

37.0 

36.25 

42.3 

41.3 

40.4 

39.6 

38.75 

45.0 

44.0 

43.0 

42.1 

41.25 

47.7 

46.7 

45.7 

44.7 

43.75 

50.5 

49.3 

48.3 

47.2 

46.25 

53.2 

52.0 

50.9 

49.8 

48.75 ■ 

55.9 

54.7 

53.5 

52.3 

51.25 ■ 

58.6 

57.3 

56.1 

54.9 

53.75 • 

61.4 

60.0 

58.7 

57.4 

56.25 - 

64.1 

62.7 

61.3 

60.0 

58.75 ■ 

66.8 

65.3 

63.9 

62.6 

61.25 - 

69.5 

68.0 

66.5 

65.1 

63.75 ■ 

72.3 

70.7 

69.1 

67.7 

66.25 - 

75.0 

73.3 

71.7 

70.2 

68.75 - 

77.7 

76.0 

74.3 

72.8 

71.25 - 

80.5 

78.7 

77.0 

75.3 

73.75 - 

83.2 

81.3 

79.6 

77.9 

76.25 - 

85.9 

84.0 

82.2 

80.4 

78.75 - 

88.6 

86.7 

84.8 

83.0 

81.25 - 

91.4 

89.3 

87.4 

85.5 

83.75 - 

94.1 

92.0 

90.0 

88.1 

86.25 - 

96.8 

94.7 

92.6 

90.6 

88.75 - 

99.5 

97.3 

95.2 

93.2 

91.25 - 

102.3 

100.0 

97.8 

95.7 

93.75 - 

105.0 

102.7 

100.4 

98.3 

96.25 - 

107.7 

105.3 

103.0 

100.9 

98.75 - 

110.5 

108.0 

105.7 

103.4 

101.25 - 

113.2 

110.7 

108.3 

106.0 

103.75 - 

115.9 

113.3 

iio.9 

108.5 

106.25 - 

118.6 

116.0 

113.5 

111.1 

108.75 - 


118.7 

116.1 

113.6 

111.25 - 



118.7 

116.2 

113.75 - 






118.7 

116.25 - 








118.75 












diff. P 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 

27 

28 


29 


3C 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 


41 


42 


43 


44 


45 


46 


47 


48 


52 
























































































































































47 ° 



Reciprocal 

M 

Reciprocal 

P 

0 

101.314 

69.315 

1 

5 

.294 

2 

5 

.272 

3 

5 

.251 

4 

6 

.229 

5 

6 

.207 

6 

6 

.186 

7 

6 

.164 

8 

7 

.143 

9 

7 

.121 

10 

101.317 

69.099 

11 

8 

.078 

12 

8 

.056 

13 

8 

.035 

14 

9 

69.013 

15 

9 

68.991 

16 

9 

.970 

17 

.319 

.948 

18 

.320 

.926 

19 

0 

.905 

20 

101.320 

68.883 

21 

1 

.861 

22 

1 

.840 

23 

1 

.818 

24 

1 

.796 

25 

2 

.775 

26 

2 

.753 

27 

2 

.731 

28 

3 

.709 

29 

3 

.688 

30 

101.323 

68.666 

31 

4 

.644 

32 

4 

• .622 

33 

4 

.601 

34 

4 

.579 

35 

5 

.557 

36 

5 

.535 

37 

5 

.514 

38 

6 

.492 

39 

6 

.470 

40 

101.326 

68.448 

41 

7 

.427 

42 

7 

.405 

43 

7 

.383 

44 

8 

.361 

45 

8 

.339 

46 

8 

.318 

47 

8 

.296 

48 

9 

.274 

49 

9 

.252 

50 

101.329 

68.230 

51 

330 

.208 

52 

0 

.186 

53 

0 

.165 

54 

0 

.143 

55 

1 

.121 

56 

1 

.099 

57 

1 

.077 

58 

2 

.055 

59 

2 

.033 

60 

101.332 

68.011 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

21 

22 

// 

2.9 

n 

2.7 

0 

1 

8.6 

8.2 

2 

14.3 

13.6 

3 

20.0 

19.1 

4 

25.7 

24.5 

5 

31.4 

30.0 

6 

37.1 

35.5 

7 

42.9 

40.9 

8 

48.6 

46.4 

9 

54.3 

51.8 

10 

60.0 

57.3 

11 

65.7 

62.7 

12 

71.4 

68.2 

13 

77.1 

73.6 

14 

82.9 

79.1 

15 

88.6 

84.5 

16 

94.3 

90.0 

17 

100.0 

95.5 

18 

105.7 

100.9 

19 

111.4 

106.4 

20 

21 

117.1 

111.8 


117.3 

22 






Log. M 

Log. P 

A 


7.9943292 

8.1591715 

0 


79 

3066 

1 


66 

4417 

2 : 


53 

5769 

3 


40 

7123 

4 


28 

8476 

5 


15 

.1599831 

O 


.9943202 

.1601187 

7 


.9943189 

2544 

8 


76 

3900 

9 


7.9943163 

8.1605259 

10 


51 

6618 

11 


38 

7977 

12 


25 

.1609337 

13 


.9943112 

.1610699 

14 


.9943099 

2061 

15 


86 

3423 

15 


74 

4787 

17 


61 

6151 

m 


48 

7517 

19 


7.9943035 

8.1618882 

20 


22 

.1620249 

21 


.9943009 

1617 

22 


.9942997 

2985 

23 


84 

4354 

24 


71 

5724 

.25 


58 

7095 

26 


45 

8466 

27 


32 

.1629839 

28 


20 

.1631212 

29 


7.9942907 

' 8.1632586 

30 * 


.9942894 

3961 

31 


81 

5336 

32 : 


68 

6713 

33 


56 

8090 

34 


43 

.1639468 

35 


30 

.1640847 

36 


17 

2227 

37 


.9942804 

3607 

38 


.9942791 

4988 

39 


7.9942779 

8.1646371. 

40 


66 

7753 

41 


53 

.1649137 

42 


40 

.1650521 

43 


27 

1907 

44 


15 

3292 

45 


.9942702 

4680 

46 


.9942689 

6068 

47 


76 

7455 

48 


63 

.1658845 

49 


7.9942651 

8.1660236 

50 


38 

1627.' 

51 


25 

3018 

52 : 


.9942612 

4411 

53 ; 


.9942599 

5805 

54 ' 


86 

7199 

55 


74 

8593 

56 


61 

.1669990 

57 


48 

.1671387 

58 ; 


35 

2784 

59 


7.9942522 

8.1674182 

60 


53 





































































48 ' 


t 

M 

P 

/ 

0 

.0098685 

.0147034 

0 

1 

5 

082 

1 

2 

5 

129 

2 

3 

4 

176 

3 

4 

4 

224 

4 

5 

4 

271 

5 

6 

4 

319 

6 

7 

3 

367 

7 

; 8 

3 

414 

8 

~9 

3 

462 

9 

10 

.0098682 

.0147510 

10 

11 

2 

558 

11 

12 

2 

606 

12 

13 

1 

653 

13 

14 

1 

701 

14 

15 

1 

749 

15 

16 

1 

797 

16 

17 

0 

845 

17 

18 

0 

894 

18 

19 

.0098680 

942 

19 

20 

.0098679 

.0147990 

20 

21 

9 

.0148038 

21 

22 

9 

087 

22 

23 

9 

135 

23 

: 24 

8 

183 

24 

25 

8 

232 

25 

26 

8 

280 

26 

27 

7 

329 

27 

28 

7 

377 

28 

29 

7 

426 

29 

30 

.0098677 

.0148474 

30 

31 

6 

523 

31 

32 

6 

572 

32 

33 

6 

621 

33 

54 

5 

670 

34 

35 

5 

718 

35 

36 

5 

767 

36 

57 

5 

816 

37 

38 

4 

865 

38 

39 

4 

914 

39 

40 

.0098674 

.0148963 

40 

41 

3 

.0149013 

41 

42 

3 

062 

42 

43 

3 

111 

43 

44 

2 

160 

44 

45 

2 

210 

45 

46 

2 

259 

46 

• 47 

2 

308 

47 

48 

1 

358 

48 

49 

1 

407 

49 

; 50 

.0098671 

.0149457 

50 

. 51 

0 

506 

51 

52 

0 

556 

52 

53 

0 

606 

53 

54 

.0098670 

656 

54 

55 

.0098669 

705 

55 

56 

9 

755 

56 

57 

9 

805 

57 

. 58 

8 

855 

58 

59 

8 

905 

59 

60 

.0098668 

.0149955 

60 


Interpolating Table. 


Tabular Differences. 


47 

48 

49 

50 

// 

// 

// 

// 

1.3 

1.25 

1.2 

1.2 

3.8 

3.75 

3.7 

3.6 

6.4 

6.25 

6.1 

6.0 

8.9 

8.75 

8.6 

8.4 

11.5 

11.25 

11.0 

10.8 

14.0 

13.75 

13.5 

13.2 

16.6 

16.25 

15.9 

15.6 

19.1 

18.75 

18.4 

18.0 

21.7 

21.25 

20.8 

20.4 

24.3 

23.75 

23.3 

22.8 

26.8 

26.25 

25.7 

25.2 

29.4 

28.75 

28.2 

27.6 

31.9 

31.25 

30.6 

30.0 

34.5 

33.75 

33.1 

32.4 

37.0 

36.25 

35.5 

34.8 

39.6 

38.75 

38.0 

37.2 

42.1 

41.25 

40.4 

39.6 

44.7 

43.75 

42.9 

42.0 

47.2 

46.25 

45.3 

44.4 

49.8 

48.75 

47.8 

46.8 

52.3 

51.25 

50.2 

49.2 

54.9 

53.75 

52.7 

51.6 

57.4 

56.25 

55.1 

54.0 

60.0 

58.75 

57.6 

56.4 

62.6 

61.25 

60 . 0 ^ 

58.8 

65.1 

63.75 

62.4 

61.2 

67.7 

66.25 

64.9 

63.6 

70.2 

68.75 

67.3 

66.0 

72.8 

71.25 

69.8 

68.4 

75.3 

73.75 

72.2 

70.8 

77.9 

76.25 

74.7 

73.2 

80.4 

78.75 

77.1 

75.6 

83.0 

81.25 

79.6 

78.0 

85.5 

83.75 

82.0 

80.4 

88.1 

86.25 

84.5 

82.8 

90.6 

88.75 

86.9 

85.2 

93.2 

91.25 

89.4 

87.6 • 

95.7 

93.75 

91.8 

90.0 

98.3 

96.25 

94.3 

92.4 

100.9 

98.75 

96.7 

94.8 

103.4 

101.25 

99.2 

97.2 

106.0 

103.75 

101.6 

99.6 

108.5 

106.25 

104.1 

102.0 

111.1 

108.75 

106.5 

104.4 

113.6 

111.25 

109 0 

106.8 ' 

116.2 

113.75 

111.4 

109.2 ■ 

118.7 

116.25 

113.9 

111.6 ■ 


118.75 

116.3 

114.0 



118.8 

116.4 




118.8 









diff.P 


- 1 

- 2 

- 3 

- 4 

- 5 

6 

- 7 

8 

- 9 

- 10 

- 11 

- 12 

- 13 

- 14 

- 15 

- 16 

- 17 

- 18 

- 19 

20 

21 

■ 22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 • 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 


50 


54 

























































































































































































f 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


/ 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 


48 ° 


Reciprocal 

P 


Log. M 


68.011 

67.989 

.968 

.946 

.924 

.902 

.880 

.858 

.836 

.814 

67.792 

.770 

.748 

.726 

.704 

.682 

.660 

.638 

.616 

.594 

67.572 

.550 

.528 

.506 

.484 

.462 

.440 

.418 

.396 

.374 

67.352 

.330 

.307 

.285 

.263 

.241 

.219 

.197 

.175 

.153 

67.131 

.108 

.086 

.064 

.042 

67.020 

66.998 

.975 

.953 

.931 

66.909 

.887 

.865 

.842 

.820 

.798 

.776 

.753 

.731 

.709 

66.687 


Reciprocal P 
Interpolating Table. 


Tabular Differences. 

diff. 
rep. P 

21 

22 

23 

// 

2.9 

// 

2.7 

// 

2.6 

0 

1 

8.6 

8.2 

7.8 

2 

14.3 

13.6 

13.0 

3 

20.0 

19.1 

18.3 

4 

25.7 

24.5 

23.5 

5 

31.4 

30.0 

28.7 

6 

37.1 

35.5 

33.9 

7 

42.9 

40.9 

39.1 

8 

48.6 

46.4 

44.3 

9 

54.3 

51.8 

49.6 

10 

60.0 

57.3 

54.8 

11 

65.7 

62.7 

60.0 

12 

71.4 

68.2 

65.2 

13 

77.1 

73.6 

70.4 

14 

82.9 

79.1 

75.7 

15 

88.6 

84.5 

80.9 

16 

94.3 

90.0 

86.1 

17 

100.0 

95.5 

91.3 

18 

105.7 

100.9 

96.5 

19 

111.4 

106.4 

101.7 

20 

117.1 

111.8 

107.0 

21 


117.3 

112.2 

22 




117.4 

23 







7.9942522 

.9942510 

.9942497 

84 

71 


8.1674182 

5582 

6982 

8382 

.1679784 


58 

46 

33 

20 

.9942407 


7.9942394 

82 

69 

56 

43 


30 

18 

.9942305 

.9942292 

79 


7.9942266 

54 

41 

28 

15 


.9942203 

.9942190 

77 

64 

51 


7.9942139 

26 

13 

.9942100 

.9942088 

75 

62 

49 

36 

24 


7.9942011 

.9941998 

85 

73 

60 

47 

34 

22 

.9941909 

.9941896 


7.9941883 

71 

58 

45 

32 


20 

.9941807 

.9941794 

81 

68 

7.9941756 



























































































49 ° 


P 

Interpolating Table. 



M 

0 

.0098668 

1 

8 

2 

7 

3 

7 

4 

7 

5 

6 

6 

6 

7 

6 

8 

6 

9 

5 

10 

.0098665 

11 

5 

12 

4 

13 

4 

14 

4 

15 

4 

16 

3 

17 

3 

18 

3 

19 

2 

20 

.0098662 

21 

2 

22 

1 

23 

1 

24 

1 

25 

1 

26 

0 

27 

0 

28 

.0098660 

29 

.0098659 

30 

.0098659 

31 

9 

32 

9 

33 

8 

34 

8 

35 

8 

36 

7 

37 

7 

38 

7 

39 

7 

40 

.0098656 

41 

6 

42 

6 

43 

5 

44 

5 

45 

5 

46 

5 

47 

4 

48 

4 

49 

4 

50 

.0098653 

51 

3 

52 

3 

53 

3 

54 

2 

55 

2 

56 

2 

57 

1 

58 

1 

59 

1 

60 

.0098650 


P 

/ 

0149955 

0 

0150005 

1 

055 

2 

105 

3 

155 

4 

206 

5 

256 

6 

306 

7 

357 

8 

407 

9 

.0150458 

10 

508 

11 

559 

12 

609 

13 

660 

14 

711 

15 

761 

16 

812 

17 

863 

18 

914 

19 

.0150965 

20 

.0151016 

21 

067 

22 

118 

23 

169 

24 

220 

25 

271 

26 

323 

27 

374 

28 

426 

29 

.0151477 

30 

528 

31 

580 

32 

631 

33 

683 

34 

735 

35 

786 

36 

838 

37 

890 

38 

942 

39 

.0151994 

40 

.0152046 

41 

098 

42 

150 

43 

202 

44 

254 

45 

306 

46 

358 

47 

411 

48 

463 

49 

.0152515 

50 

568 

51 

620 

52 

673 

53 

725 

54 

778 

55 

831 

56 

883 

57 

936 

58 

.0152989 

59 

.0153042 

60 


i 


Tabular Differences. 

diff. P 

50 

51 

52 

53 

n 

1.2 

// 

1.2 

it 

1.2 

it 

l.i 

0 

1 

3.6 

3.5 

3.5 

3.4 

2 

6.0 

5.9 

5.8 

5 7 

3 

8 4 

8 2 

8 1 

7 9 

4 

10.8 

10.6 

10.4 

10.2 

5 

13.2 

12.9 

12.7 

12.5 

6 

15.6 

15.3 

15.0 

14.7 

7 

18.0 

17.6 

17.3 

17.0 

8 

20.4 

20.0 

19.6 

19.2 

9 

22.8 

22.4 

21.9 

21.5 

10 

OK O 

24.7 

24.2 

23.8 

Zo Z 

11 

27.6 

27.1 

26.5 

26.0 

12 

30.0 

29.4 

28.8 

28.3 

13 

32.4 

31.8 

31.2 

30.6 

14 

34.8 

34.1 

33.5 

32.8 

15 

37.2 

38.5 

35.8 

35.1 

16 

39.6 

38.8 

38.1 

37.4 

17 

42.0 

41.2 

40.4 

39.6 

18 

44.4 

43.5 

42.7 

41.9 

19 

46.8 

45.9 

45.0 

44.2 

20 

49.2 

48.2 

47.3 

46.4 

21 

51.6 

50.6 

49.6 

48 7 

22 

54.0 

52.9 

51.9 

50.9 

23 

56.4 

55.3 

54.2 

53.2 

24 

58.8 

57.6 

56.5 

55.5 

25 

61.2 

60.0 

58.8 

57.7 

26 

63.6 

62.4 

61.2 

60.0 

27 

66.0 

64.7 

63 5 

" 62:3 

28 

29 

68.4 

67.1 

65 8 

64 5 

70 8 

69 4 

68 1 

66 8 

30 

73 2 

71 8 

70 4 

69 1 

31 

75 6 

74 1 

72 7 

71 3 

32 

78 0 

76 5 

7K ft 

73 6 

/DU 

_ 33 

34 

~35 

80 4 

78 8 

. 77 3 

75.8 

82.8 

81.2 

79.6 

78.1 

85 2 

83.5 

81 9 

80.4 

36 

87.6 

85.9 

84.2 

82.6 

37 

90.0 

88.2 

86.5 

84.9 

38 

92.4 

90.6 

88.8 

87.2 

39 

94.8 

92.9 

91.2 

89 4 

40 

97 2 

95.3 

93.5 

91.7 

41 

99.6 

97.6 

95.8 

94.0 

42 

102.0 

100.0 

98.1 

96.2 

43 

104.4 

102.4 

100.4 

98.5 

44 

106.8 

104.7 

102.7 

100.8 

45 

109.2 

107.1 

105.0 

103.0 

46 

111 6 

109.4 

107.3 

105.3 

47 

114. a 

111.8 

109,6 

107.5 

48 

116.4 

114.1 

111.9 

109.8 

49 

118.8 

116.5 

114.2 

112.1 • 

50 


118.8 

116.5 

114 3 


51 



118.8 

116.6 



52 




118.9 




53 






56 




























































































































































































i 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56. 

57 

58 

59 

60 


8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52’ 

53 

54 

55 

56 

57 

58 

59 

60 


49 ° 


3 


101.350 

0 

1 

1 

1 


Reciprocal 

P 


66.687 

.664 

.642 

.620 

.598 

.575 

.553 

.531 

.509 

.486 


Log. M 



n 


.9941756 

43 

30 

17 

.9941705 


8.1759607 

.1761056 

2506 

3957 

5410 


.9941692 

79 

66 

54 

41 


6863 

8316 

.1769771 

.1771226 

2682 


66-464 

.442 

.419 

.397 

.375 

.352 

.330 

.308 

.285 

.263 

66-241 

.218 

.196 

.173 

.151 

.129 

.106 

.084 

.062 

.039 

66.017 

65-994 

.972 

.949 

.927 


.905 

.882 

.860 

.837 

.815 

65.792 

.770 

.747 

.725 

.702 

.680 

.657 

.635 

.612 

.590 


Reciprocal P 
Interpolating Table. 


Tabular Diff. 

diff. 
rep. P 

22 

23 

' // 

2 7 

2.6 

0 

1 

• 2 

8.2 

7.8 

13.6 

13.0 

3 

19.1 

18.3 

4 

24.5 

23.5 

5 

30.0 

28.7 

6 

35.5 

33.9 

7 

8 

40.9 

39.1 

46.4 

44.3 

9 

51.8 

4Q 

t ±V . 1 ) 

10 

57.3 

54.8 

11 

62.7 

60.0 

12 

13 

14 

68.2 

65.2 

73.6 

70.4 

79.1 

75.7 

15 

00 

80.9 

16 

90.0 

86.1 

17 

i.5.5 

91.3 

18 

100.9 

96.5 

19 

106.4 

101.7 

20 

111.8 

107.0 

21 

117.3 

112.2 

22 


117.4 

23 








65.567 

.545 

.522 

.500 

.477 


.454 

.432 

.409 

.387 

.364 

65.342 


7.9941628 

16 

.9941603 

.9941590 

77 

65 

52 

39 

26 

14 

7.9941501 

.9941488 

75 

63 

50 

37 

25 

.9941412 

.9941399 

86 

7.9941374 

61 

48 

36 

23 

.9941310 

.9941297 

85 

72 

59 

7.9941246 

34 

. 21 
.9941208 
.9941196 

83 

70 

58 

45 

32 

7.9941120 

.9941107 

.9941094 

81 

69 

56 

43 

31 

18 

.9941006 

7.9940993 


8.1774139 

5598 

7057 

8517 

.1779977 

.1781438 

2901 

4364 

5828 

7293 

8.1788759 
.1790226 
1692 
3161 
4631 

6101 
7571 
.1799043 
.1800516 
1990 

8.1803464 
4939 
6416 
7893 
.1809370 

.1810849 

2329 

3810 

5291 

6774 

8.1818257 

.1819741 

.1821227 

2712 

4199 

5686 
7175 
.1828664 
.1830154 
1646 

8.1833138 

4630 

6124 

7619 

.1839115 

.1840611 

2108 

3606 

5106 

6606 

8.1848106 


57 






















































































I 
































































































































































- . 




' 






















. 



♦ « 
























✓ 












LIBRARY OF CONGRESS 






